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

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

Evaluate

$$10x+29$$

Solution Steps

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

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

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

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

Multiply -10 and -1 to get 10.

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

Consider \left(x-2\right)\left(x+2\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 2.

$$x^{2}+10x+25-\left(x^{2}-4\right)$$

To find the opposite of x^{2}-4, find the opposite of each term.

$$x^{2}+10x+25-x^{2}+4$$

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

$$10x+25+4$$

Add 25 and 4 to get 29.

$$10x+29$$

Expand

$$10x+29$$

Solution Steps

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

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

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

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

Multiply -10 and -1 to get 10.

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

Consider \left(x-2\right)\left(x+2\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 2.

$$x^{2}+10x+25-\left(x^{2}-4\right)$$

To find the opposite of x^{2}-4, find the opposite of each term.

$$x^{2}+10x+25-x^{2}+4$$

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

$$10x+25+4$$

Add 25 and 4 to get 29.

$$10x+29$$