Solve =(x-5)^2-(x-7)(x+2)+9+5x

$$= ( x - 5 ) ^ { 2 } - ( x - 7 ) ( x + 2 ) + 9 + 5 x$$

Evaluate

$$48$$

Solution Steps

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

$$x^{2}-10x+25-\left(x-7\right)\left(x+2\right)+9+5x$$

Use the distributive property to multiply x-7 by x+2 and combine like terms.

$$x^{2}-10x+25-\left(x^{2}-5x-14\right)+9+5x$$

To find the opposite of x^{2}-5x-14, find the opposite of each term.

$$x^{2}-10x+25-x^{2}+5x+14+9+5x$$

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

$$-10x+25+5x+14+9+5x$$

Combine -10x and 5x to get -5x.

$$-5x+25+14+9+5x$$

Add 25 and 14 to get 39.

$$-5x+39+9+5x$$

Add 39 and 9 to get 48.

$$-5x+48+5x$$

Combine -5x and 5x to get 0.

$$48$$

Factor

$$2^{4}\times 3$$