Solve 6(x+y)^2-2(x-y)(x+y)=

$$6 ( x + y ) ^ { 2 } - 2 ( x - y ) ( x + y ) =$$

Evaluate

$$4\left(x+y\right)\left(x+2y\right)$$

Solution Steps

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

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

Use the distributive property to multiply 6 by x^{2}+2xy+y^{2}.

$$6x^{2}+12xy+6y^{2}-2\left(x-y\right)\left(x+y\right)$$

Use the distributive property to multiply -2 by x-y.

$$6x^{2}+12xy+6y^{2}+\left(-2x+2y\right)\left(x+y\right)$$

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

$$6x^{2}+12xy+6y^{2}-2x^{2}+2y^{2}$$

Combine 6x^{2} and -2x^{2} to get 4x^{2}.

$$4x^{2}+12xy+6y^{2}+2y^{2}$$

Combine 6y^{2} and 2y^{2} to get 8y^{2}.

$$4x^{2}+12xy+8y^{2}$$

Expand

$$4x^{2}+12xy+8y^{2}$$

Solution Steps

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

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

Use the distributive property to multiply 6 by x^{2}+2xy+y^{2}.

$$6x^{2}+12xy+6y^{2}-2\left(x-y\right)\left(x+y\right)$$

Use the distributive property to multiply -2 by x-y.

$$6x^{2}+12xy+6y^{2}+\left(-2x+2y\right)\left(x+y\right)$$

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

$$6x^{2}+12xy+6y^{2}-2x^{2}+2y^{2}$$

Combine 6x^{2} and -2x^{2} to get 4x^{2}.

$$4x^{2}+12xy+6y^{2}+2y^{2}$$

Combine 6y^{2} and 2y^{2} to get 8y^{2}.

$$4x^{2}+12xy+8y^{2}$$