Simplify (6/5x^2-2x-3/5)(6/5x^2-2/5x+3/4)

Math
(65×2-2x-35)(65×2-25x+34)
Simplify terms.
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Combine 65 and x2.
(6×25-2x-35)(65×2-25x+34)
Simplify each term.
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Combine 65 and x2.
(6×25-2x-35)(6×25-25x+34)
Combine x and 25.
(6×25-2x-35)(6×25-x⋅25+34)
Move 2 to the left of x.
(6×25-2x-35)(6×25-2×5+34)
(6×25-2x-35)(6×25-2×5+34)
(6×25-2x-35)(6×25-2×5+34)
Expand (6×25-2x-35)(6×25-2×5+34) by multiplying each term in the first expression by each term in the second expression.
6×25⋅6×25+6×25(-2×5)+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Simplify each term.
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Multiply 6×25⋅6×25.
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Multiply 6×25 and 6×25.
6×2(6×2)5⋅5+6×25(-2×5)+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply 6 by 6.
36x2x25⋅5+6×25(-2×5)+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply x2 by x2 by adding the exponents.
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Move x2.
36(x2x2)5⋅5+6×25(-2×5)+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Use the power rule aman=am+n to combine exponents.
36×2+25⋅5+6×25(-2×5)+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Add 2 and 2.
36×45⋅5+6×25(-2×5)+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
36×45⋅5+6×25(-2×5)+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply 5 by 5.
36×425+6×25(-2×5)+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
36×425+6×25(-2×5)+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Rewrite using the commutative property of multiplication.
36×425-6×25⋅2×5+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply -6×25⋅2×5.
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Multiply 2×5 and 6×25.
36×425-2x(6×2)5⋅5+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply 6 by 2.
36×425-12x⋅x25⋅5+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply x by x2 by adding the exponents.
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Move x2.
36×425-12(x2x)5⋅5+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply x2 by x.
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Raise x to the power of 1.
36×425-12(x2x1)5⋅5+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Use the power rule aman=am+n to combine exponents.
36×425-12×2+15⋅5+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
36×425-12×2+15⋅5+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Add 2 and 1.
36×425-12×35⋅5+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
36×425-12×35⋅5+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply 5 by 5.
36×425-12×325+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
36×425-12×325+6×25⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Cancel the common factor of 2.
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Factor 2 out of 6×2.
36×425-12×325+2(3×2)5⋅34-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Factor 2 out of 4.
36×425-12×325+2(3×2)5⋅32(2)-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Cancel the common factor.
36×425-12×325+2(3×2)5⋅32⋅2-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Rewrite the expression.
36×425-12×325+3×25⋅32-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
36×425-12×325+3×25⋅32-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply 3×25 and 32.
36×425-12×325+3×2⋅35⋅2-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply 3 by 3.
36×425-12×325+9×25⋅2-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply 5 by 2.
36×425-12×325+9×210-2x6x25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply -2x6x25.
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Combine -2 and 6×25.
36×425-12×325+9×210+x-2(6×2)5-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply 6 by -2.
36×425-12×325+9×210+x-12×25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Combine x and -12×25.
36×425-12×325+9×210+x(-12×2)5-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Raise x to the power of 1.
36×425-12×325+9×210+-12(x1x2)5-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Use the power rule aman=am+n to combine exponents.
36×425-12×325+9×210+-12×1+25-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Add 1 and 2.
36×425-12×325+9×210+-12×35-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
36×425-12×325+9×210+-12×35-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Move the negative in front of the fraction.
36×425-12×325+9×210-(12)x35-2x(-2×5)-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply -2x(-2×5).
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Multiply -1 by -2.
36×425-12×325+9×210-12×35+2x2x5-2×34-35⋅6×25-35(-2×5)-35⋅34
Combine 2 and 2×5.
36×425-12×325+9×210-12×35+x2(2x)5-2×34-35⋅6×25-35(-2×5)-35⋅34
Multiply 2 by 2.
36×425-12×325+9×210-12×35+x4x5-2×34-35⋅6×25-35(-2×5)-35⋅34
Combine x and 4×5.
36×425-12×325+9×210-12×35+x(4x)5-2×34-35⋅6×25-35(-2×5)-35⋅34
Raise x to the power of 1.
36×425-12×325+9×210-12×35+4(x1x)5-2×34-35⋅6×25-35(-2×5)-35⋅34
Raise x to the power of 1.
36×425-12×325+9×210-12×35+4(x1x1)5-2×34-35⋅6×25-35(-2×5)-35⋅34
Use the power rule aman=am+n to combine exponents.
36×425-12×325+9×210-12×35+4×1+15-2×34-35⋅6×25-35(-2×5)-35⋅34
Add 1 and 1.
36×425-12×325+9×210-12×35+4×25-2×34-35⋅6×25-35(-2×5)-35⋅34
36×425-12×325+9×210-12×35+4×25-2×34-35⋅6×25-35(-2×5)-35⋅34
Cancel the common factor of 2.
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Factor 2 out of -2x.
36×425-12×325+9×210-12×35+4×25+2(-x)34-35⋅6×25-35(-2×5)-35⋅34
Factor 2 out of 4.
36×425-12×325+9×210-12×35+4×25+2(-x)32(2)-35⋅6×25-35(-2×5)-35⋅34
Cancel the common factor.
36×425-12×325+9×210-12×35+4×25+2(-x)32⋅2-35⋅6×25-35(-2×5)-35⋅34
Rewrite the expression.
36×425-12×325+9×210-12×35+4×25-x32-35⋅6×25-35(-2×5)-35⋅34
36×425-12×325+9×210-12×35+4×25-x32-35⋅6×25-35(-2×5)-35⋅34
Combine 32 and x.
36×425-12×325+9×210-12×35+4×25-3×2-35⋅6×25-35(-2×5)-35⋅34
Multiply -35⋅6×25.
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Multiply 6×25 and 35.
36×425-12×325+9×210-12×35+4×25-3×2-6×2⋅35⋅5-35(-2×5)-35⋅34
Multiply 3 by 6.
36×425-12×325+9×210-12×35+4×25-3×2-18×25⋅5-35(-2×5)-35⋅34
Multiply 5 by 5.
36×425-12×325+9×210-12×35+4×25-3×2-18×225-35(-2×5)-35⋅34
36×425-12×325+9×210-12×35+4×25-3×2-18×225-35(-2×5)-35⋅34
Multiply -35(-2×5).
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Multiply -1 by -1.
36×425-12×325+9×210-12×35+4×25-3×2-18×225+1(35)2×5-35⋅34
Multiply 35 by 1.
36×425-12×325+9×210-12×35+4×25-3×2-18×225+35⋅2×5-35⋅34
Multiply 35 and 2×5.
36×425-12×325+9×210-12×35+4×25-3×2-18×225+3(2x)5⋅5-35⋅34
Multiply 2 by 3.
36×425-12×325+9×210-12×35+4×25-3×2-18×225+6×5⋅5-35⋅34
Multiply 5 by 5.
36×425-12×325+9×210-12×35+4×25-3×2-18×225+6×25-35⋅34
36×425-12×325+9×210-12×35+4×25-3×2-18×225+6×25-35⋅34
Multiply -35⋅34.
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Multiply 34 and 35.
36×425-12×325+9×210-12×35+4×25-3×2-18×225+6×25-3⋅34⋅5
Multiply 3 by 3.
36×425-12×325+9×210-12×35+4×25-3×2-18×225+6×25-94⋅5
Multiply 4 by 5.
36×425-12×325+9×210-12×35+4×25-3×2-18×225+6×25-920
36×425-12×325+9×210-12×35+4×25-3×2-18×225+6×25-920
36×425-12×325+9×210-12×35+4×25-3×2-18×225+6×25-920
To write -12×35 as a fraction with a common denominator, multiply by 55.
36×425+9×210-12×325-12×35⋅55+4×25-3×2-18×225+6×25-920
Write each expression with a common denominator of 25, by multiplying each by an appropriate factor of 1.
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Multiply 12×35 and 55.
36×425+9×210-12×325-12×3⋅55⋅5+4×25-3×2-18×225+6×25-920
Multiply 5 by 5.
36×425+9×210-12×325-12×3⋅525+4×25-3×2-18×225+6×25-920
36×425+9×210-12×325-12×3⋅525+4×25-3×2-18×225+6×25-920
Combine the numerators over the common denominator.
36×425+9×210+-12×3-12×3⋅525+4×25-3×2-18×225+6×25-920
Simplify each term.
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Simplify the numerator.
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Factor 12×3 out of -12×3-12×3⋅5.
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Factor 12×3 out of -12×3.
36×425+9×210+12×3(-1)-12×3⋅525+4×25-3×2-18×225+6×25-920
Factor 12×3 out of -12×3⋅5.
36×425+9×210+12×3(-1)+12×3(-1⋅5)25+4×25-3×2-18×225+6×25-920
Factor 12×3 out of 12×3(-1)+12×3(-1⋅5).
36×425+9×210+12×3(-1-1⋅5)25+4×25-3×2-18×225+6×25-920
36×425+9×210+12×3(-1-1⋅5)25+4×25-3×2-18×225+6×25-920
Multiply -1 by 5.
36×425+9×210+12×3(-1-5)25+4×25-3×2-18×225+6×25-920
Subtract 5 from -1.
36×425+9×210+12×3⋅-625+4×25-3×2-18×225+6×25-920
36×425+9×210+12×3⋅-625+4×25-3×2-18×225+6×25-920
Multiply -6 by 12.
36×425+9×210+-72×325+4×25-3×2-18×225+6×25-920
Move the negative in front of the fraction.
36×425+9×210-72×325+4×25-3×2-18×225+6×25-920
36×425+9×210-72×325+4×25-3×2-18×225+6×25-920
To write 4×25 as a fraction with a common denominator, multiply by 22.
36×425-72×325+9×210+4×25⋅22-3×2-18×225+6×25-920
Write each expression with a common denominator of 10, by multiplying each by an appropriate factor of 1.
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Multiply 4×25 and 22.
36×425-72×325+9×210+4×2⋅25⋅2-3×2-18×225+6×25-920
Multiply 5 by 2.
36×425-72×325+9×210+4×2⋅210-3×2-18×225+6×25-920
36×425-72×325+9×210+4×2⋅210-3×2-18×225+6×25-920
Combine the numerators over the common denominator.
36×425-72×325+9×2+4×2⋅210-3×2-18×225+6×25-920
Simplify each term.
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Simplify the numerator.
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Factor x2 out of 9×2+4×2⋅2.
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Factor x2 out of 9×2.
36×425-72×325+x2⋅9+4×2⋅210-3×2-18×225+6×25-920
Factor x2 out of 4×2⋅2.
36×425-72×325+x2⋅9+x2(4⋅2)10-3×2-18×225+6×25-920
Factor x2 out of x2⋅9+x2(4⋅2).
36×425-72×325+x2(9+4⋅2)10-3×2-18×225+6×25-920
36×425-72×325+x2(9+4⋅2)10-3×2-18×225+6×25-920
Multiply 4 by 2.
36×425-72×325+x2(9+8)10-3×2-18×225+6×25-920
Add 9 and 8.
36×425-72×325+x2⋅1710-3×2-18×225+6×25-920
36×425-72×325+x2⋅1710-3×2-18×225+6×25-920
Move 17 to the left of x2.
36×425-72×325+17×210-3×2-18×225+6×25-920
36×425-72×325+17×210-3×2-18×225+6×25-920
To write 17×210 as a fraction with a common denominator, multiply by 55.
36×425-72×325-3×2+17×210⋅55-18×225+6×25-920
To write -18×225 as a fraction with a common denominator, multiply by 22.
36×425-72×325-3×2+17×210⋅55-18×225⋅22+6×25-920
Write each expression with a common denominator of 50, by multiplying each by an appropriate factor of 1.
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Multiply 17×210 and 55.
36×425-72×325-3×2+17×2⋅510⋅5-18×225⋅22+6×25-920
Multiply 10 by 5.
36×425-72×325-3×2+17×2⋅550-18×225⋅22+6×25-920
Multiply 18×225 and 22.
36×425-72×325-3×2+17×2⋅550-18×2⋅225⋅2+6×25-920
Multiply 25 by 2.
36×425-72×325-3×2+17×2⋅550-18×2⋅250+6×25-920
36×425-72×325-3×2+17×2⋅550-18×2⋅250+6×25-920
Combine the numerators over the common denominator.
36×425-72×325-3×2+17×2⋅5-18×2⋅250+6×25-920
Simplify each term.
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Simplify the numerator.
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Factor x2 out of 17×2⋅5-18×2⋅2.
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Factor x2 out of 17×2⋅5.
36×425-72×325-3×2+x2(17⋅5)-18×2⋅250+6×25-920
Factor x2 out of -18×2⋅2.
36×425-72×325-3×2+x2(17⋅5)+x2(-18⋅2)50+6×25-920
Factor x2 out of x2(17⋅5)+x2(-18⋅2).
36×425-72×325-3×2+x2(17⋅5-18⋅2)50+6×25-920
36×425-72×325-3×2+x2(17⋅5-18⋅2)50+6×25-920
Multiply 17 by 5.
36×425-72×325-3×2+x2(85-18⋅2)50+6×25-920
Multiply -18 by 2.
36×425-72×325-3×2+x2(85-36)50+6×25-920
Subtract 36 from 85.
36×425-72×325-3×2+x2⋅4950+6×25-920
36×425-72×325-3×2+x2⋅4950+6×25-920
Move 49 to the left of x2.
36×425-72×325-3×2+49×250+6×25-920
36×425-72×325-3×2+49×250+6×25-920
To write -3×2 as a fraction with a common denominator, multiply by 2525.
36×425-72×325+49×250-3×2⋅2525+6×25-920
To write 6×25 as a fraction with a common denominator, multiply by 22.
36×425-72×325+49×250-3×2⋅2525+6×25⋅22-920
Write each expression with a common denominator of 50, by multiplying each by an appropriate factor of 1.
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Multiply 3×2 and 2525.
36×425-72×325+49×250-3x⋅252⋅25+6×25⋅22-920
Multiply 2 by 25.
36×425-72×325+49×250-3x⋅2550+6×25⋅22-920
Multiply 6×25 and 22.
36×425-72×325+49×250-3x⋅2550+6x⋅225⋅2-920
Multiply 25 by 2.
36×425-72×325+49×250-3x⋅2550+6x⋅250-920
36×425-72×325+49×250-3x⋅2550+6x⋅250-920
Combine the numerators over the common denominator.
36×425-72×325+49×250+-3x⋅25+6x⋅250-920
Simplify each term.
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Simplify the numerator.
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Factor 3x out of -3x⋅25+6x⋅2.
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Factor 3x out of -3x⋅25.
36×425-72×325+49×250+3x(-1⋅25)+6x⋅250-920
Factor 3x out of 6x⋅2.
36×425-72×325+49×250+3x(-1⋅25)+3x(2⋅2)50-920
Factor 3x out of 3x(-1⋅25)+3x(2⋅2).
36×425-72×325+49×250+3x(-1⋅25+2⋅2)50-920
36×425-72×325+49×250+3x(-1⋅25+2⋅2)50-920
Combine exponents.
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Multiply -1 by 25.
36×425-72×325+49×250+3x(-25+2⋅2)50-920
Multiply 2 by 2.
36×425-72×325+49×250+3x(-25+4)50-920
36×425-72×325+49×250+3x(-25+4)50-920
Add -25 and 4.
36×425-72×325+49×250+3x⋅-2150-920
36×425-72×325+49×250+3x⋅-2150-920
Multiply -21 by 3.
36×425-72×325+49×250+-63×50-920
Move the negative in front of the fraction.
36×425-72×325+49×250-63×50-920
36×425-72×325+49×250-63×50-920
Simplify (6/5x^2-2x-3/5)(6/5x^2-2/5x+3/4)

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