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

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

Evaluate

$$\left(3x-2y\right)\left(4y-x\right)$$

Solution Steps

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

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

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

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

To find the opposite of 4x^{2}-12xy+9y^{2}, find the opposite of each term.

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

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

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

Combine 2xy and 12xy to get 14xy.

$$-3x^{2}+14xy+y^{2}-9y^{2}$$

Combine y^{2} and -9y^{2} to get -8y^{2}.

$$-3x^{2}+14xy-8y^{2}$$

Expand

$$-3x^{2}+14xy-8y^{2}$$

Solution Steps

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

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

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

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

To find the opposite of 4x^{2}-12xy+9y^{2}, find the opposite of each term.

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

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

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

Combine 2xy and 12xy to get 14xy.

$$-3x^{2}+14xy+y^{2}-9y^{2}$$

Combine y^{2} and -9y^{2} to get -8y^{2}.

$$-3x^{2}+14xy-8y^{2}$$