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

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

Evaluate

$$-10x-50$$

Solution Steps

Consider \left(x+5\right)\left(x-5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 5.

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

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

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

Calculate -x to the power of 2 and get x^{2}.

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

Multiply -10 and -1 to get 10.

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

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

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

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

$$-25-10x-25$$

Subtract 25 from -25 to get -50.

$$-50-10x$$

Expand

$$-10x-50$$

Solution Steps

Consider \left(x+5\right)\left(x-5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 5.

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

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

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

Calculate -x to the power of 2 and get x^{2}.

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

Multiply -10 and -1 to get 10.

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

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

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

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

$$-25-10x-25$$

Subtract 25 from -25 to get -50.

$$-50-10x$$