Solve 8(x-3y)^2+4(x-3y)

$$8 ( x - 3 y ) ^ { 2 } + 4 ( x - 3 y )$$

Evaluate

$$4\left(x-3y\right)\left(2x-6y+1\right)$$

Solution Steps

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

$$8\left(x^{2}-6xy+9y^{2}\right)+4\left(x-3y\right)$$

Use the distributive property to multiply 8 by x^{2}-6xy+9y^{2}.

$$8x^{2}-48xy+72y^{2}+4\left(x-3y\right)$$

Use the distributive property to multiply 4 by x-3y.

$$8x^{2}-48xy+72y^{2}+4x-12y$$

Expand

$$8x^{2}-48xy+4x+72y^{2}-12y$$

Solution Steps

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

$$8\left(x^{2}-6xy+9y^{2}\right)+4\left(x-3y\right)$$

Use the distributive property to multiply 8 by x^{2}-6xy+9y^{2}.

$$8x^{2}-48xy+72y^{2}+4\left(x-3y\right)$$

Use the distributive property to multiply 4 by x-3y.

$$8x^{2}-48xy+72y^{2}+4x-12y$$