Solve f(x)=-2(x+4)^2+72

$$f ( x ) = - 2 ( x + 4 ) ^ { 2 } + 72$$

Evaluate

$$2\left(2-x\right)\left(x+10\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$-2\left(x^{2}+8x+16\right)+72$$

Use the distributive property to multiply -2 by x^{2}+8x+16.

$$-2x^{2}-16x-32+72$$

Add -32 and 72 to get 40.

$$-2x^{2}-16x+40$$

Expand

$$40-16x-2x^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$-2\left(x^{2}+8x+16\right)+72$$

Use the distributive property to multiply -2 by x^{2}+8x+16.

$$-2x^{2}-16x-32+72$$

Add -32 and 72 to get 40.

$$-2x^{2}-16x+40$$