Solve 9(x-2y)^2-(x-2y)

$$9 ( x - 2 y ) ^ { 2 } - ( x - 2 y )$$

Evaluate

$$\left(x-2y\right)\left(9x-18y-1\right)$$

Solution Steps

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

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

Use the distributive property to multiply 9 by x^{2}-4xy+4y^{2}.

$$9x^{2}-36xy+36y^{2}-\left(x-2y\right)$$

To find the opposite of x-2y, find the opposite of each term.

$$9x^{2}-36xy+36y^{2}-x+2y$$

Expand

$$9x^{2}-36xy-x+36y^{2}+2y$$

Solution Steps

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

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

Use the distributive property to multiply 9 by x^{2}-4xy+4y^{2}.

$$9x^{2}-36xy+36y^{2}-\left(x-2y\right)$$

To find the opposite of x-2y, find the opposite of each term.

$$9x^{2}-36xy+36y^{2}-x+2y$$