Solve f(x)=-3(x+5)^2+20

$$f ( x ) = - 3 ( x + 5 ) ^ { 2 } + 20$$

Evaluate

$$-3\left(x+5\right)^{2}+20$$

Solution Steps

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

$$-3\left(x^{2}+10x+25\right)+20$$

Use the distributive property to multiply -3 by x^{2}+10x+25.

$$-3x^{2}-30x-75+20$$

Add -75 and 20 to get -55.

$$-3x^{2}-30x-55$$

Expand

$$-3x^{2}-30x-55$$

Solution Steps

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

$$-3\left(x^{2}+10x+25\right)+20$$

Use the distributive property to multiply -3 by x^{2}+10x+25.

$$-3x^{2}-30x-75+20$$

Add -75 and 20 to get -55.

$$-3x^{2}-30x-55$$