Solve (x+5)^2-(1+x)^2

$$( x + 5 ) ^ { 2 } - ( 1 + x ) ^ { 2 }$$

Evaluate

$$8\left(x+3\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$x^{2}+10x+25-\left(1+x\right)^{2}$$

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

$$x^{2}+10x+25-\left(1+2x+x^{2}\right)$$

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

$$x^{2}+10x+25-1-2x-x^{2}$$

Subtract 1 from 25 to get 24.

$$x^{2}+10x+24-2x-x^{2}$$

Combine 10x and -2x to get 8x.

$$x^{2}+8x+24-x^{2}$$

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

$$8x+24$$

Expand

$$8x+24$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$x^{2}+10x+25-\left(1+x\right)^{2}$$

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

$$x^{2}+10x+25-\left(1+2x+x^{2}\right)$$

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

$$x^{2}+10x+25-1-2x-x^{2}$$

Subtract 1 from 25 to get 24.

$$x^{2}+10x+24-2x-x^{2}$$

Combine 10x and -2x to get 8x.

$$x^{2}+8x+24-x^{2}$$

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

$$8x+24$$