Solve 8(x-y)^2-4(x+y)^2

$$8 ( x - y ) ^ { 2 } - 4 ( x + y ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

$$8\left(x^{2}-2xy+y^{2}\right)-4\left(x+y\right)^{2}$$

Use the distributive property to multiply 8 by x^{2}-2xy+y^{2}.

$$8x^{2}-16xy+8y^{2}-4\left(x+y\right)^{2}$$

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

$$8x^{2}-16xy+8y^{2}-4\left(x^{2}+2xy+y^{2}\right)$$

Use the distributive property to multiply -4 by x^{2}+2xy+y^{2}.

$$8x^{2}-16xy+8y^{2}-4x^{2}-8xy-4y^{2}$$

Combine 8x^{2} and -4x^{2} to get 4x^{2}.

$$4x^{2}-16xy+8y^{2}-8xy-4y^{2}$$

Combine -16xy and -8xy to get -24xy.

$$4x^{2}-24xy+8y^{2}-4y^{2}$$

Combine 8y^{2} and -4y^{2} to get 4y^{2}.

$$4x^{2}-24xy+4y^{2}$$

Expand

$$4x^{2}-24xy+4y^{2}$$

Solution Steps

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

$$8\left(x^{2}-2xy+y^{2}\right)-4\left(x+y\right)^{2}$$

Use the distributive property to multiply 8 by x^{2}-2xy+y^{2}.

$$8x^{2}-16xy+8y^{2}-4\left(x+y\right)^{2}$$

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

$$8x^{2}-16xy+8y^{2}-4\left(x^{2}+2xy+y^{2}\right)$$

Use the distributive property to multiply -4 by x^{2}+2xy+y^{2}.

$$8x^{2}-16xy+8y^{2}-4x^{2}-8xy-4y^{2}$$

Combine 8x^{2} and -4x^{2} to get 4x^{2}.

$$4x^{2}-16xy+8y^{2}-8xy-4y^{2}$$

Combine -16xy and -8xy to get -24xy.

$$4x^{2}-24xy+8y^{2}-4y^{2}$$

Combine 8y^{2} and -4y^{2} to get 4y^{2}.

$$4x^{2}-24xy+4y^{2}$$