Solve -0.1left(x-4right)^2(x+2)

$$-0.1 { \left(x-4 \right) }^{ 2 } (x+2)$$

Evaluate

$$-\frac{\left(x+2\right)\left(x-4\right)^{2}}{10}$$

Solution Steps

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

$$-0.1\left(x^{2}-8x+16\right)\left(x+2\right)$$

Use the distributive property to multiply -0.1 by x^{2}-8x+16.

$$\left(-0.1x^{2}+0.8x-1.6\right)\left(x+2\right)$$

Use the distributive property to multiply -0.1x^{2}+0.8x-1.6 by x+2 and combine like terms.

$$-0.1x^{3}+0.6x^{2}-3.2$$

Expand

$$-\frac{x^{3}}{10}+\frac{3x^{2}}{5}-3.2$$

Solution Steps

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

$$-0.1\left(x^{2}-8x+16\right)\left(x+2\right)$$

Use the distributive property to multiply -0.1 by x^{2}-8x+16.

$$\left(-0.1x^{2}+0.8x-1.6\right)\left(x+2\right)$$

Use the distributive property to multiply -0.1x^{2}+0.8x-1.6 by x+2 and combine like terms.

$$-0.1x^{3}+0.6x^{2}-3.2$$