Solve (x+4)(x+5)-(x-6)^2

$$( x + 4 ) ( x + 5 ) - ( x - 6 ) ^ { 2 }$$

Evaluate

$$21x-16$$

Solution Steps

Use the distributive property to multiply x+4 by x+5 and combine like terms.

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

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

$$x^{2}+9x+20-\left(x^{2}-12x+36\right)$$

To find the opposite of x^{2}-12x+36, find the opposite of each term.

$$x^{2}+9x+20-x^{2}+12x-36$$

Combine x^{2} and -x^{2} to get 0.

$$9x+20+12x-36$$

Combine 9x and 12x to get 21x.

$$21x+20-36$$

Subtract 36 from 20 to get -16.

$$21x-16$$

Expand

$$21x-16$$

Solution Steps

Use the distributive property to multiply x+4 by x+5 and combine like terms.

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

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

$$x^{2}+9x+20-\left(x^{2}-12x+36\right)$$

To find the opposite of x^{2}-12x+36, find the opposite of each term.

$$x^{2}+9x+20-x^{2}+12x-36$$

Combine x^{2} and -x^{2} to get 0.

$$9x+20+12x-36$$

Combine 9x and 12x to get 21x.

$$21x+20-36$$

Subtract 36 from 20 to get -16.

$$21x-16$$