Solve +9left(x+2right)^2-left(x+1right)^2

$$+9 { \left(x+2 \right) }^{ 2 } - { \left(x+1 \right) }^{ 2 }$$

Evaluate

$$\left(2x+5\right)\left(4x+7\right)$$

Solution Steps

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

$$9\left(x^{2}+4x+4\right)-\left(x+1\right)^{2}$$

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

$$9x^{2}+36x+36-\left(x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$9x^{2}+36x+36-\left(x^{2}+2x+1\right)$$

To find the opposite of x^{2}+2x+1, find the opposite of each term.

$$9x^{2}+36x+36-x^{2}-2x-1$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}+36x+36-2x-1$$

Combine 36x and -2x to get 34x.

$$8x^{2}+34x+36-1$$

Subtract 1 from 36 to get 35.

$$8x^{2}+34x+35$$

Expand

$$8x^{2}+34x+35$$

Solution Steps

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

$$9\left(x^{2}+4x+4\right)-\left(x+1\right)^{2}$$

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

$$9x^{2}+36x+36-\left(x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$9x^{2}+36x+36-\left(x^{2}+2x+1\right)$$

To find the opposite of x^{2}+2x+1, find the opposite of each term.

$$9x^{2}+36x+36-x^{2}-2x-1$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}+36x+36-2x-1$$

Combine 36x and -2x to get 34x.

$$8x^{2}+34x+36-1$$

Subtract 1 from 36 to get 35.

$$8x^{2}+34x+35$$