Solve left(2x-3yright)^2-9left(x-yright)^2

$${ \left(2x-3y \right) }^{ 2 } -9 { \left(x-y \right) }^{ 2 }$$

Evaluate

$$-x\left(5x-6y\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3y\right)^{2}.

$$4x^{2}-12xy+9y^{2}-9\left(x-y\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.

$$4x^{2}-12xy+9y^{2}-9\left(x^{2}-2xy+y^{2}\right)$$

Use the distributive property to multiply -9 by x^{2}-2xy+y^{2}.

$$4x^{2}-12xy+9y^{2}-9x^{2}+18xy-9y^{2}$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

$$-5x^{2}-12xy+9y^{2}+18xy-9y^{2}$$

Combine -12xy and 18xy to get 6xy.

$$-5x^{2}+6xy+9y^{2}-9y^{2}$$

Combine 9y^{2} and -9y^{2} to get 0.

$$-5x^{2}+6xy$$

Expand

$$6xy-5x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3y\right)^{2}.

$$4x^{2}-12xy+9y^{2}-9\left(x-y\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.

$$4x^{2}-12xy+9y^{2}-9\left(x^{2}-2xy+y^{2}\right)$$

Use the distributive property to multiply -9 by x^{2}-2xy+y^{2}.

$$4x^{2}-12xy+9y^{2}-9x^{2}+18xy-9y^{2}$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

$$-5x^{2}-12xy+9y^{2}+18xy-9y^{2}$$

Combine -12xy and 18xy to get 6xy.

$$-5x^{2}+6xy+9y^{2}-9y^{2}$$

Combine 9y^{2} and -9y^{2} to get 0.

$$-5x^{2}+6xy$$