Solve (x+6)^2-13(x+6)+40

$$( x + 6 ) ^ { 2 } - 13 ( x + 6 ) + 40$$

Evaluate

$$\left(x-2\right)\left(x+1\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+12x+36-13\left(x+6\right)+40$$

Use the distributive property to multiply -13 by x+6.

$$x^{2}+12x+36-13x-78+40$$

Combine 12x and -13x to get -x.

$$x^{2}-x+36-78+40$$

Subtract 78 from 36 to get -42.

$$x^{2}-x-42+40$$

Add -42 and 40 to get -2.

$$x^{2}-x-2$$

Expand

$$x^{2}-x-2$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+12x+36-13\left(x+6\right)+40$$

Use the distributive property to multiply -13 by x+6.

$$x^{2}+12x+36-13x-78+40$$

Combine 12x and -13x to get -x.

$$x^{2}-x+36-78+40$$

Subtract 78 from 36 to get -42.

$$x^{2}-x-42+40$$

Add -42 and 40 to get -2.

$$x^{2}-x-2$$