Solve (x+3y)^2-9(x+3y)+20

$$( x + 3 y ) ^ { 2 } - 9 ( x + 3 y ) + 20$$

Evaluate

$$\left(x+3y-5\right)\left(x+3y-4\right)$$

Solution Steps

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

$$x^{2}+6xy+9y^{2}-9\left(x+3y\right)+20$$

Use the distributive property to multiply -9 by x+3y.

$$x^{2}+6xy+9y^{2}-9x-27y+20$$

Expand

$$x^{2}+6xy-9x+9y^{2}-27y+20$$

Solution Steps

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

$$x^{2}+6xy+9y^{2}-9\left(x+3y\right)+20$$

Use the distributive property to multiply -9 by x+3y.

$$x^{2}+6xy+9y^{2}-9x-27y+20$$