Solve -2left(x-9right)^2(5-x)

$$-2 { \left(x-9 \right) }^{ 2 } (5-x)$$

Evaluate

$$-2\left(5-x\right)\left(x-9\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-9\right)^{2}.

$$-2\left(x^{2}-18x+81\right)\left(5-x\right)$$

Use the distributive property to multiply -2 by x^{2}-18x+81.

$$\left(-2x^{2}+36x-162\right)\left(5-x\right)$$

Use the distributive property to multiply -2x^{2}+36x-162 by 5-x and combine like terms.

$$-46x^{2}+2x^{3}+342x-810$$

Expand

$$2x^{3}-46x^{2}+342x-810$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-9\right)^{2}.

$$-2\left(x^{2}-18x+81\right)\left(5-x\right)$$

Use the distributive property to multiply -2 by x^{2}-18x+81.

$$\left(-2x^{2}+36x-162\right)\left(5-x\right)$$

Use the distributive property to multiply -2x^{2}+36x-162 by 5-x and combine like terms.

$$-46x^{2}+2x^{3}+342x-810$$