Solve (x-5)^2-(x-5)(7-2x)

$$( x - 5 ) ^ { 2 } - ( x - 5 ) ( 7 - 2 x )$$

Evaluate

$$3\left(x-5\right)\left(x-4\right)$$

Solution Steps

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

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

Use the distributive property to multiply x-5 by 7-2x and combine like terms.

$$x^{2}-10x+25-\left(17x-2x^{2}-35\right)$$

To find the opposite of 17x-2x^{2}-35, find the opposite of each term.

$$x^{2}-10x+25-17x+2x^{2}+35$$

Combine -10x and -17x to get -27x.

$$x^{2}-27x+25+2x^{2}+35$$

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$3x^{2}-27x+25+35$$

Add 25 and 35 to get 60.

$$3x^{2}-27x+60$$

Expand

$$3x^{2}-27x+60$$

Solution Steps

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

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

Use the distributive property to multiply x-5 by 7-2x and combine like terms.

$$x^{2}-10x+25-\left(17x-2x^{2}-35\right)$$

To find the opposite of 17x-2x^{2}-35, find the opposite of each term.

$$x^{2}-10x+25-17x+2x^{2}+35$$

Combine -10x and -17x to get -27x.

$$x^{2}-27x+25+2x^{2}+35$$

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$3x^{2}-27x+25+35$$

Add 25 and 35 to get 60.

$$3x^{2}-27x+60$$