Solve -2(x-45)^2+4050

$$- 2 ( x - 45 ) ^ { 2 } + 4050$$

Evaluate

$$2x\left(90-x\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-45\right)^{2}.

$$-2\left(x^{2}-90x+2025\right)+4050$$

Use the distributive property to multiply -2 by x^{2}-90x+2025.

$$-2x^{2}+180x-4050+4050$$

Add -4050 and 4050 to get 0.

$$-2x^{2}+180x$$

Expand

$$180x-2x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-45\right)^{2}.

$$-2\left(x^{2}-90x+2025\right)+4050$$

Use the distributive property to multiply -2 by x^{2}-90x+2025.

$$-2x^{2}+180x-4050+4050$$

Add -4050 and 4050 to get 0.

$$-2x^{2}+180x$$