Solve 2x-y^2+(4x-3y)^2+10(x-y)(x+y)+10xy]:(-6x)

$$2 x - y ^ { 2 } + ( 4 x - 3 y ) ^ { 2 } + 10 ( x - y ) ( x + y ) + 10 x y ] : ( - 6 x )$$

Evaluate

$$2\left(13x^{2}-7xy+x-y^{2}\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-3y\right)^{2}.

$$2x-y^{2}+16x^{2}-24xy+9y^{2}+10\left(x-y\right)\left(x+y\right)+10xy$$

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

$$2x+8y^{2}+16x^{2}-24xy+10\left(x-y\right)\left(x+y\right)+10xy$$

Use the distributive property to multiply 10 by x-y.

$$2x+8y^{2}+16x^{2}-24xy+\left(10x-10y\right)\left(x+y\right)+10xy$$

Use the distributive property to multiply 10x-10y by x+y and combine like terms.

$$2x+8y^{2}+16x^{2}-24xy+10x^{2}-10y^{2}+10xy$$

Combine 16x^{2} and 10x^{2} to get 26x^{2}.

$$2x+8y^{2}+26x^{2}-24xy-10y^{2}+10xy$$

Combine 8y^{2} and -10y^{2} to get -2y^{2}.

$$2x-2y^{2}+26x^{2}-24xy+10xy$$

Combine -24xy and 10xy to get -14xy.

$$2x-2y^{2}+26x^{2}-14xy$$

Expand

$$26x^{2}-14xy+2x-2y^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-3y\right)^{2}.

$$2x-y^{2}+16x^{2}-24xy+9y^{2}+10\left(x-y\right)\left(x+y\right)+10xy$$

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

$$2x+8y^{2}+16x^{2}-24xy+10\left(x-y\right)\left(x+y\right)+10xy$$

Use the distributive property to multiply 10 by x-y.

$$2x+8y^{2}+16x^{2}-24xy+\left(10x-10y\right)\left(x+y\right)+10xy$$

Use the distributive property to multiply 10x-10y by x+y and combine like terms.

$$2x+8y^{2}+16x^{2}-24xy+10x^{2}-10y^{2}+10xy$$

Combine 16x^{2} and 10x^{2} to get 26x^{2}.

$$2x+8y^{2}+26x^{2}-24xy-10y^{2}+10xy$$

Combine 8y^{2} and -10y^{2} to get -2y^{2}.

$$2x-2y^{2}+26x^{2}-24xy+10xy$$

Combine -24xy and 10xy to get -14xy.

$$2x-2y^{2}+26x^{2}-14xy$$