Solve 4+12left(x-yright)+9left(x-yright)^2

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

Evaluate

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

Solution Steps

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

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}.

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