Simplify (3/2x-2/3)(-2/3x-4)

Math
(32x-23)(-23x-4)
Simplify terms.
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Combine 32 and x.
(3×2-23)(-23x-4)
Simplify each term.
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Combine x and 23.
(3×2-23)(-x⋅23-4)
Move 2 to the left of x.
(3×2-23)(-2×3-4)
(3×2-23)(-2×3-4)
(3×2-23)(-2×3-4)
Expand (3×2-23)(-2×3-4) using the FOIL Method.
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Apply the distributive property.
3×2(-2×3-4)-23(-2×3-4)
Apply the distributive property.
3×2(-2×3)+3×2⋅-4-23(-2×3-4)
Apply the distributive property.
3×2(-2×3)+3×2⋅-4-23(-2×3)-23⋅-4
3×2(-2×3)+3×2⋅-4-23(-2×3)-23⋅-4
Simplify and combine like terms.
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Simplify each term.
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Rewrite using the commutative property of multiplication.
-3×2⋅2×3+3×2⋅-4-23(-2×3)-23⋅-4
Cancel the common factor of 3.
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Move the leading negative in -3×2 into the numerator.
-3×2⋅2×3+3×2⋅-4-23(-2×3)-23⋅-4
Factor 3 out of -3x.
3(-x)2⋅2×3+3×2⋅-4-23(-2×3)-23⋅-4
Cancel the common factor.
3(-x)2⋅2×3+3×2⋅-4-23(-2×3)-23⋅-4
Rewrite the expression.
-x2(2x)+3×2⋅-4-23(-2×3)-23⋅-4
-x2(2x)+3×2⋅-4-23(-2×3)-23⋅-4
Cancel the common factor of 2.
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Factor 2 out of 2x.
-x2(2(x))+3×2⋅-4-23(-2×3)-23⋅-4
Cancel the common factor.
-x2(2x)+3×2⋅-4-23(-2×3)-23⋅-4
Rewrite the expression.
-x⋅x+3×2⋅-4-23(-2×3)-23⋅-4
-x⋅x+3×2⋅-4-23(-2×3)-23⋅-4
Raise x to the power of 1.
-(x1x)+3×2⋅-4-23(-2×3)-23⋅-4
Raise x to the power of 1.
-(x1x1)+3×2⋅-4-23(-2×3)-23⋅-4
Use the power rule aman=am+n to combine exponents.
-x1+1+3×2⋅-4-23(-2×3)-23⋅-4
Add 1 and 1.
-x2+3×2⋅-4-23(-2×3)-23⋅-4
Cancel the common factor of 2.
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Factor 2 out of -4.
-x2+3×2⋅(2(-2))-23(-2×3)-23⋅-4
Cancel the common factor.
-x2+3×2⋅(2⋅-2)-23(-2×3)-23⋅-4
Rewrite the expression.
-x2+3x⋅-2-23(-2×3)-23⋅-4
-x2+3x⋅-2-23(-2×3)-23⋅-4
Multiply -2 by 3.
-x2-6x-23(-2×3)-23⋅-4
Multiply -23(-2×3).
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Multiply -1 by -1.
-x2-6x+1(23)2×3-23⋅-4
Multiply 23 by 1.
-x2-6x+23⋅2×3-23⋅-4
Multiply 23 and 2×3.
-x2-6x+2(2x)3⋅3-23⋅-4
Multiply 2 by 2.
-x2-6x+4×3⋅3-23⋅-4
Multiply 3 by 3.
-x2-6x+4×9-23⋅-4
-x2-6x+4×9-23⋅-4
Multiply -23⋅-4.
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Multiply -4 by -1.
-x2-6x+4×9+4(23)
Combine 4 and 23.
-x2-6x+4×9+4⋅23
Multiply 4 by 2.
-x2-6x+4×9+83
-x2-6x+4×9+83
-x2-6x+4×9+83
To write -6x as a fraction with a common denominator, multiply by 99.
-x2-6x⋅99+4×9+83
Combine -6x and 99.
-x2+-6x⋅99+4×9+83
Combine the numerators over the common denominator.
-x2+-6x⋅9+4×9+83
To write -x2 as a fraction with a common denominator, multiply by 99.
-x2⋅99+-6x⋅9+4×9+83
Combine -x2 and 99.
-x2⋅99+-6x⋅9+4×9+83
Combine the numerators over the common denominator.
-x2⋅9-6x⋅9+4×9+83
To write 83 as a fraction with a common denominator, multiply by 33.
-x2⋅9-6x⋅9+4×9+83⋅33
Write each expression with a common denominator of 9, by multiplying each by an appropriate factor of 1.
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Multiply 83 and 33.
-x2⋅9-6x⋅9+4×9+8⋅33⋅3
Multiply 3 by 3.
-x2⋅9-6x⋅9+4×9+8⋅39
-x2⋅9-6x⋅9+4×9+8⋅39
Combine the numerators over the common denominator.
-x2⋅9-6x⋅9+4x+8⋅39
-x2⋅9-6x⋅9+4x+8⋅39
Simplify the numerator.
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Multiply 9 by -1.
-9×2-6x⋅9+4x+8⋅39
Multiply 9 by -6.
-9×2-54x+4x+8⋅39
Multiply 8 by 3.
-9×2-54x+4x+249
Add -54x and 4x.
-9×2-50x+249
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-9⋅24=-216 and whose sum is b=-50.
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Factor -50 out of -50x.
-9×2-50(x)+249
Rewrite -50 as 4 plus -54
-9×2+(4-54)x+249
Apply the distributive property.
-9×2+4x-54x+249
-9×2+4x-54x+249
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(-9×2+4x)-54x+249
Factor out the greatest common factor (GCF) from each group.
x(-9x+4)+6(-9x+4)9
x(-9x+4)+6(-9x+4)9
Factor the polynomial by factoring out the greatest common factor, -9x+4.
(-9x+4)(x+6)9
(-9x+4)(x+6)9
(-9x+4)(x+6)9
Simplify with factoring out.
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Factor -1 out of -9x.
(-(9x)+4)(x+6)9
Rewrite 4 as -1(-4).
(-(9x)-1(-4))(x+6)9
Factor -1 out of -(9x)-1(-4).
-(9x-4)(x+6)9
Simplify the expression.
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Rewrite -(9x-4) as -1(9x-4).
-1(9x-4)(x+6)9
Move the negative in front of the fraction.
-(9x-4)(x+6)9
-(9x-4)(x+6)9
-(9x-4)(x+6)9
Simplify (3/2x-2/3)(-2/3x-4)

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