Simplify (3x^5-7x^4+2)^2x^2

Math
(3×5-7×4+2)2×2
Rewrite (3×5-7×4+2)2 as (3×5-7×4+2)(3×5-7×4+2).
(3×5-7×4+2)(3×5-7×4+2)x2
Expand (3×5-7×4+2)(3×5-7×4+2) by multiplying each term in the first expression by each term in the second expression.
(3×5(3×5)+3×5(-7×4)+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Simplify terms.
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Simplify each term.
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Rewrite using the commutative property of multiplication.
(3⋅3(x5x5)+3×5(-7×4)+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Multiply x5 by x5 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
(3⋅3×5+5+3×5(-7×4)+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Add 5 and 5.
(3⋅3×10+3×5(-7×4)+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
(3⋅3×10+3×5(-7×4)+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Multiply 3 by 3.
(9×10+3×5(-7×4)+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Rewrite using the commutative property of multiplication.
(9×10+3⋅-7(x5x4)+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Multiply x5 by x4 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
(9×10+3⋅-7×5+4+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Add 5 and 4.
(9×10+3⋅-7×9+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
(9×10+3⋅-7×9+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Multiply 3 by -7.
(9×10-21×9+3×5⋅2-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Multiply 2 by 3.
(9×10-21×9+6×5-7×4(3×5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Rewrite using the commutative property of multiplication.
(9×10-21×9+6×5-7⋅3(x4x5)-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Multiply x4 by x5 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
(9×10-21×9+6×5-7⋅3×4+5-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Add 4 and 5.
(9×10-21×9+6×5-7⋅3×9-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
(9×10-21×9+6×5-7⋅3×9-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Multiply -7 by 3.
(9×10-21×9+6×5-21×9-7×4(-7×4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Rewrite using the commutative property of multiplication.
(9×10-21×9+6×5-21×9-7⋅-7(x4x4)-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Multiply x4 by x4 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
(9×10-21×9+6×5-21×9-7⋅-7×4+4-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Add 4 and 4.
(9×10-21×9+6×5-21×9-7⋅-7×8-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
(9×10-21×9+6×5-21×9-7⋅-7×8-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Multiply -7 by -7.
(9×10-21×9+6×5-21×9+49×8-7×4⋅2+2(3×5)+2(-7×4)+2⋅2)x2
Multiply 2 by -7.
(9×10-21×9+6×5-21×9+49×8-14×4+2(3×5)+2(-7×4)+2⋅2)x2
Multiply 3 by 2.
(9×10-21×9+6×5-21×9+49×8-14×4+6×5+2(-7×4)+2⋅2)x2
Multiply -7 by 2.
(9×10-21×9+6×5-21×9+49×8-14×4+6×5-14×4+2⋅2)x2
Multiply 2 by 2.
(9×10-21×9+6×5-21×9+49×8-14×4+6×5-14×4+4)x2
(9×10-21×9+6×5-21×9+49×8-14×4+6×5-14×4+4)x2
Simplify terms.
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Subtract 21×9 from -21×9.
(9×10-42×9+6×5+49×8-14×4+6×5-14×4+4)x2
Add 6×5 and 6×5.
(9×10-42×9+12×5+49×8-14×4-14×4+4)x2
Subtract 14×4 from -14×4.
(9×10-42×9+12×5+49×8-28×4+4)x2
Apply the distributive property.
9x10x2-42x9x2+12x5x2+49x8x2-28x4x2+4×2
9x10x2-42x9x2+12x5x2+49x8x2-28x4x2+4×2
9x10x2-42x9x2+12x5x2+49x8x2-28x4x2+4×2
Simplify.
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Multiply x10 by x2 by adding the exponents.
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Move x2.
9(x2x10)-42x9x2+12x5x2+49x8x2-28x4x2+4×2
Use the power rule aman=am+n to combine exponents.
9×2+10-42x9x2+12x5x2+49x8x2-28x4x2+4×2
Add 2 and 10.
9×12-42x9x2+12x5x2+49x8x2-28x4x2+4×2
9×12-42x9x2+12x5x2+49x8x2-28x4x2+4×2
Multiply x9 by x2 by adding the exponents.
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Move x2.
9×12-42(x2x9)+12x5x2+49x8x2-28x4x2+4×2
Use the power rule aman=am+n to combine exponents.
9×12-42×2+9+12x5x2+49x8x2-28x4x2+4×2
Add 2 and 9.
9×12-42×11+12x5x2+49x8x2-28x4x2+4×2
9×12-42×11+12x5x2+49x8x2-28x4x2+4×2
Multiply x5 by x2 by adding the exponents.
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Move x2.
9×12-42×11+12(x2x5)+49x8x2-28x4x2+4×2
Use the power rule aman=am+n to combine exponents.
9×12-42×11+12×2+5+49x8x2-28x4x2+4×2
Add 2 and 5.
9×12-42×11+12×7+49x8x2-28x4x2+4×2
9×12-42×11+12×7+49x8x2-28x4x2+4×2
Multiply x8 by x2 by adding the exponents.
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Move x2.
9×12-42×11+12×7+49(x2x8)-28x4x2+4×2
Use the power rule aman=am+n to combine exponents.
9×12-42×11+12×7+49×2+8-28x4x2+4×2
Add 2 and 8.
9×12-42×11+12×7+49×10-28x4x2+4×2
9×12-42×11+12×7+49×10-28x4x2+4×2
Multiply x4 by x2 by adding the exponents.
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Move x2.
9×12-42×11+12×7+49×10-28(x2x4)+4×2
Use the power rule aman=am+n to combine exponents.
9×12-42×11+12×7+49×10-28×2+4+4×2
Add 2 and 4.
9×12-42×11+12×7+49×10-28×6+4×2
9×12-42×11+12×7+49×10-28×6+4×2
9×12-42×11+12×7+49×10-28×6+4×2
Move 12×7.
9×12-42×11+49×10+12×7-28×6+4×2
Simplify (3x^5-7x^4+2)^2x^2

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