Solve 12(x-y)^2+7(x-y)-12

$$12 ( x - y ) ^ { 2 } + 7 ( x - y ) - 12$$

Evaluate

$$\left(4x-4y-3\right)\left(3x-3y+4\right)$$

Solution Steps

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

$$12\left(x^{2}-2xy+y^{2}\right)+7\left(x-y\right)-12$$

Use the distributive property to multiply 12 by x^{2}-2xy+y^{2}.

$$12x^{2}-24xy+12y^{2}+7\left(x-y\right)-12$$

Use the distributive property to multiply 7 by x-y.

$$12x^{2}-24xy+12y^{2}+7x-7y-12$$

Expand

$$12x^{2}-24xy+7x+12y^{2}-7y-12$$

Solution Steps

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

$$12\left(x^{2}-2xy+y^{2}\right)+7\left(x-y\right)-12$$

Use the distributive property to multiply 12 by x^{2}-2xy+y^{2}.

$$12x^{2}-24xy+12y^{2}+7\left(x-y\right)-12$$

Use the distributive property to multiply 7 by x-y.

$$12x^{2}-24xy+12y^{2}+7x-7y-12$$