Simplify (2x-3y)^3-(2x+3y)^3

Math
(2x-3y)3-(2x+3y)3
Simplify each term.
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Use the Binomial Theorem.
(2x)3+3(2x)2(-3y)+3(2x)(-3y)2+(-3y)3-(2x+3y)3
Simplify each term.
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Apply the product rule to 2x.
23×3+3(2x)2(-3y)+3(2x)(-3y)2+(-3y)3-(2x+3y)3
Raise 2 to the power of 3.
8×3+3(2x)2(-3y)+3(2x)(-3y)2+(-3y)3-(2x+3y)3
Rewrite using the commutative property of multiplication.
8×3+3⋅-3((2x)2y)+3(2x)(-3y)2+(-3y)3-(2x+3y)3
Multiply 3 by -3.
8×3-9((2x)2y)+3(2x)(-3y)2+(-3y)3-(2x+3y)3
Apply the product rule to 2x.
8×3-9(22x2y)+3(2x)(-3y)2+(-3y)3-(2x+3y)3
Raise 2 to the power of 2.
8×3-9(4x2y)+3(2x)(-3y)2+(-3y)3-(2x+3y)3
Multiply 4 by -9.
8×3-36(x2y)+3(2x)(-3y)2+(-3y)3-(2x+3y)3
Multiply 2 by 3.
8×3-36x2y+6x(-3y)2+(-3y)3-(2x+3y)3
Apply the product rule to -3y.
8×3-36x2y+6x((-3)2y2)+(-3y)3-(2x+3y)3
Rewrite using the commutative property of multiplication.
8×3-36x2y+6⋅(-3)2(xy2)+(-3y)3-(2x+3y)3
Raise -3 to the power of 2.
8×3-36x2y+6⋅9(xy2)+(-3y)3-(2x+3y)3
Multiply 6 by 9.
8×3-36x2y+54(xy2)+(-3y)3-(2x+3y)3
Apply the product rule to -3y.
8×3-36x2y+54xy2+(-3)3y3-(2x+3y)3
Raise -3 to the power of 3.
8×3-36x2y+54xy2-27y3-(2x+3y)3
8×3-36x2y+54xy2-27y3-(2x+3y)3
Use the Binomial Theorem.
8×3-36x2y+54xy2-27y3-((2x)3+3(2x)2(3y)+3(2x)(3y)2+(3y)3)
Simplify each term.
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Apply the product rule to 2x.
8×3-36x2y+54xy2-27y3-(23×3+3(2x)2(3y)+3(2x)(3y)2+(3y)3)
Raise 2 to the power of 3.
8×3-36x2y+54xy2-27y3-(8×3+3(2x)2(3y)+3(2x)(3y)2+(3y)3)
Rewrite using the commutative property of multiplication.
8×3-36x2y+54xy2-27y3-(8×3+3⋅3((2x)2y)+3(2x)(3y)2+(3y)3)
Multiply 3 by 3.
8×3-36x2y+54xy2-27y3-(8×3+9((2x)2y)+3(2x)(3y)2+(3y)3)
Apply the product rule to 2x.
8×3-36x2y+54xy2-27y3-(8×3+9(22x2y)+3(2x)(3y)2+(3y)3)
Raise 2 to the power of 2.
8×3-36x2y+54xy2-27y3-(8×3+9(4x2y)+3(2x)(3y)2+(3y)3)
Multiply 4 by 9.
8×3-36x2y+54xy2-27y3-(8×3+36(x2y)+3(2x)(3y)2+(3y)3)
Multiply 2 by 3.
8×3-36x2y+54xy2-27y3-(8×3+36x2y+6x(3y)2+(3y)3)
Apply the product rule to 3y.
8×3-36x2y+54xy2-27y3-(8×3+36x2y+6x(32y2)+(3y)3)
Rewrite using the commutative property of multiplication.
8×3-36x2y+54xy2-27y3-(8×3+36x2y+6⋅32(xy2)+(3y)3)
Raise 3 to the power of 2.
8×3-36x2y+54xy2-27y3-(8×3+36x2y+6⋅9(xy2)+(3y)3)
Multiply 6 by 9.
8×3-36x2y+54xy2-27y3-(8×3+36x2y+54(xy2)+(3y)3)
Apply the product rule to 3y.
8×3-36x2y+54xy2-27y3-(8×3+36x2y+54xy2+33y3)
Raise 3 to the power of 3.
8×3-36x2y+54xy2-27y3-(8×3+36x2y+54xy2+27y3)
8×3-36x2y+54xy2-27y3-(8×3+36x2y+54xy2+27y3)
Apply the distributive property.
8×3-36x2y+54xy2-27y3-(8×3)-(36x2y)-(54xy2)-(27y3)
Simplify.
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Multiply 8 by -1.
8×3-36x2y+54xy2-27y3-8×3-(36x2y)-(54xy2)-(27y3)
Multiply 36 by -1.
8×3-36x2y+54xy2-27y3-8×3-36(x2y)-(54xy2)-(27y3)
Multiply 54 by -1.
8×3-36x2y+54xy2-27y3-8×3-36(x2y)-54(xy2)-(27y3)
Multiply 27 by -1.
8×3-36x2y+54xy2-27y3-8×3-36(x2y)-54(xy2)-27y3
8×3-36x2y+54xy2-27y3-8×3-36(x2y)-54(xy2)-27y3
Remove parentheses.
8×3-36x2y+54xy2-27y3-8×3-36x2y-54xy2-27y3
8×3-36x2y+54xy2-27y3-8×3-36x2y-54xy2-27y3
Simplify by adding terms.
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Combine the opposite terms in 8×3-36x2y+54xy2-27y3-8×3-36x2y-54xy2-27y3.
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Subtract 8×3 from 8×3.
-36x2y+54xy2-27y3+0-36x2y-54xy2-27y3
Add -36x2y+54xy2-27y3 and 0.
-36x2y+54xy2-27y3-36x2y-54xy2-27y3
Subtract 54xy2 from 54xy2.
-36x2y-27y3-36x2y+0-27y3
Add -36x2y-27y3-36x2y and 0.
-36x2y-27y3-36x2y-27y3
-36x2y-27y3-36x2y-27y3
Subtract 36x2y from -36x2y.
-27y3-72x2y-27y3
Subtract 27y3 from -27y3.
-54y3-72x2y
-54y3-72x2y
Simplify (2x-3y)^3-(2x+3y)^3

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