Solve (x-3y)^2-5(x-3y)+6

$$( x - 3 y ) ^ { 2 } - 5 ( x - 3 y ) + 6$$

Evaluate

$$\left(x-3y-3\right)\left(x-3y-2\right)$$

Solution Steps

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

$$x^{2}-6xy+9y^{2}-5\left(x-3y\right)+6$$

Use the distributive property to multiply -5 by x-3y.

$$x^{2}-6xy+9y^{2}-5x+15y+6$$

Expand

$$x^{2}-6xy-5x+9y^{2}+15y+6$$

Solution Steps

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

$$x^{2}-6xy+9y^{2}-5\left(x-3y\right)+6$$

Use the distributive property to multiply -5 by x-3y.

$$x^{2}-6xy+9y^{2}-5x+15y+6$$