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

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

Evaluate

$$\left(x+3y\right)\left(5x+y\right)$$

Solution Steps

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

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

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

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

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

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

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

$$5x^{2}+12xy+4y^{2}+4xy-y^{2}$$

Combine 12xy and 4xy to get 16xy.

$$5x^{2}+16xy+4y^{2}-y^{2}$$

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

$$5x^{2}+16xy+3y^{2}$$

Expand

$$5x^{2}+16xy+3y^{2}$$

Solution Steps

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

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

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

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

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

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

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

$$5x^{2}+12xy+4y^{2}+4xy-y^{2}$$

Combine 12xy and 4xy to get 16xy.

$$5x^{2}+16xy+4y^{2}-y^{2}$$

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

$$5x^{2}+16xy+3y^{2}$$