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

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

Evaluate

$$20x$$

Solution Steps

Multiply x+5 and x+5 to get \left(x+5\right)^{2}.

$$\left(x+5\right)^{2}-\left(x-5\right)^{2}$$

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

$$x^{2}+10x+25-\left(x-5\right)^{2}$$

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

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

To find the opposite of x^{2}-10x+25, find the opposite of each term.

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

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

$$10x+25+10x-25$$

Combine 10x and 10x to get 20x.

$$20x+25-25$$

Subtract 25 from 25 to get 0.

$$20x$$

Expand

$$20x$$

Solution Steps

Multiply x+5 and x+5 to get \left(x+5\right)^{2}.

$$\left(x+5\right)^{2}-\left(x-5\right)^{2}$$

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

$$x^{2}+10x+25-\left(x-5\right)^{2}$$

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

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

To find the opposite of x^{2}-10x+25, find the opposite of each term.

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

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

$$10x+25+10x-25$$

Combine 10x and 10x to get 20x.

$$20x+25-25$$

Subtract 25 from 25 to get 0.

$$20x$$