Solve f(x)=(x-5)^2-2(x-5)(x+3)

$$f ( x ) = ( x - 5 ) ^ { 2 } - 2 ( x - 5 ) ( x + 3 )$$

Evaluate

$$-\left(x-5\right)\left(x+11\right)$$

Solution Steps

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

$$x^{2}-10x+25-2\left(x-5\right)\left(x+3\right)$$

Use the distributive property to multiply -2 by x-5.

$$x^{2}-10x+25+\left(-2x+10\right)\left(x+3\right)$$

Use the distributive property to multiply -2x+10 by x+3 and combine like terms.

$$x^{2}-10x+25-2x^{2}+4x+30$$

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

$$-x^{2}-10x+25+4x+30$$

Combine -10x and 4x to get -6x.

$$-x^{2}-6x+25+30$$

Add 25 and 30 to get 55.

$$-x^{2}-6x+55$$

Expand

$$55-6x-x^{2}$$

Solution Steps

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

$$x^{2}-10x+25-2\left(x-5\right)\left(x+3\right)$$

Use the distributive property to multiply -2 by x-5.

$$x^{2}-10x+25+\left(-2x+10\right)\left(x+3\right)$$

Use the distributive property to multiply -2x+10 by x+3 and combine like terms.

$$x^{2}-10x+25-2x^{2}+4x+30$$

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

$$-x^{2}-10x+25+4x+30$$

Combine -10x and 4x to get -6x.

$$-x^{2}-6x+25+30$$

Add 25 and 30 to get 55.

$$-x^{2}-6x+55$$