Solve (1)4+12(x-y)+9(x-y)^2=

$$( 1 ) 4 + 12 ( x - y ) + 9 ( x - y ) ^ { 2 } =$$

Evaluate

$$\left(3x-3y+2\right)^{2}$$

Solution Steps

Multiply 1 and 4 to get 4.

$$4+12\left(x-y\right)+9\left(x-y\right)^{2}$$

Use the distributive property to multiply 12 by x-y.

$$4+12x-12y+9\left(x-y\right)^{2}$$

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

$$4+12x-12y+9\left(x^{2}-2xy+y^{2}\right)$$

Use the distributive property to multiply 9 by x^{2}-2xy+y^{2}.

$$4+12x-12y+9x^{2}-18xy+9y^{2}$$

Expand

$$9x^{2}-18xy+12x+9y^{2}-12y+4$$

Solution Steps

Multiply 1 and 4 to get 4.

$$4+12\left(x-y\right)+9\left(x-y\right)^{2}$$

Use the distributive property to multiply 12 by x-y.

$$4+12x-12y+9\left(x-y\right)^{2}$$

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

$$4+12x-12y+9\left(x^{2}-2xy+y^{2}\right)$$

Use the distributive property to multiply 9 by x^{2}-2xy+y^{2}.

$$4+12x-12y+9x^{2}-18xy+9y^{2}$$