Solve (3x+y)^2-(2x-y)^2-5x(x-y)

$$( 3 x + y ) ^ { 2 } - ( 2 x - y ) ^ { 2 } - 5 x ( x - y )$$

Evaluate

$$15xy$$

Solution Steps

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

$$9x^{2}+6xy+y^{2}-\left(2x-y\right)^{2}-5x\left(x-y\right)$$

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

$$9x^{2}+6xy+y^{2}-\left(4x^{2}-4xy+y^{2}\right)-5x\left(x-y\right)$$

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

$$9x^{2}+6xy+y^{2}-4x^{2}+4xy-y^{2}-5x\left(x-y\right)$$

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

$$5x^{2}+6xy+y^{2}+4xy-y^{2}-5x\left(x-y\right)$$

Combine 6xy and 4xy to get 10xy.

$$5x^{2}+10xy+y^{2}-y^{2}-5x\left(x-y\right)$$

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

$$5x^{2}+10xy-5x\left(x-y\right)$$

Use the distributive property to multiply -5x by x-y.

$$5x^{2}+10xy-5x^{2}+5xy$$

Combine 5x^{2} and -5x^{2} to get 0.

$$10xy+5xy$$

Combine 10xy and 5xy to get 15xy.

$$15xy$$

Expand

$$15xy$$

Solution Steps

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

$$9x^{2}+6xy+y^{2}-\left(2x-y\right)^{2}-5x\left(x-y\right)$$

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

$$9x^{2}+6xy+y^{2}-\left(4x^{2}-4xy+y^{2}\right)-5x\left(x-y\right)$$

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

$$9x^{2}+6xy+y^{2}-4x^{2}+4xy-y^{2}-5x\left(x-y\right)$$

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

$$5x^{2}+6xy+y^{2}+4xy-y^{2}-5x\left(x-y\right)$$

Combine 6xy and 4xy to get 10xy.

$$5x^{2}+10xy+y^{2}-y^{2}-5x\left(x-y\right)$$

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

$$5x^{2}+10xy-5x\left(x-y\right)$$

Use the distributive property to multiply -5x by x-y.

$$5x^{2}+10xy-5x^{2}+5xy$$

Combine 5x^{2} and -5x^{2} to get 0.

$$10xy+5xy$$

Combine 10xy and 5xy to get 15xy.

$$15xy$$