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

$$( 2 x - 3 y ) ^ { 2 } - ( x + y ) ( x - 2 y )$$

Evaluate

$$3x^{2}-11xy+11y^{2}$$

Solution Steps

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

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

Use the distributive property to multiply x+y by x-2y and combine like terms.

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

To find the opposite of x^{2}-xy-2y^{2}, find the opposite of each term.

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

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}-12xy+9y^{2}+xy+2y^{2}$$

Combine -12xy and xy to get -11xy.

$$3x^{2}-11xy+9y^{2}+2y^{2}$$

Combine 9y^{2} and 2y^{2} to get 11y^{2}.

$$3x^{2}-11xy+11y^{2}$$

Expand

$$3x^{2}-11xy+11y^{2}$$

Solution Steps

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

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

Use the distributive property to multiply x+y by x-2y and combine like terms.

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

To find the opposite of x^{2}-xy-2y^{2}, find the opposite of each term.

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

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}-12xy+9y^{2}+xy+2y^{2}$$

Combine -12xy and xy to get -11xy.

$$3x^{2}-11xy+9y^{2}+2y^{2}$$

Combine 9y^{2} and 2y^{2} to get 11y^{2}.

$$3x^{2}-11xy+11y^{2}$$