Solve -3.2left(x-4right)^2(x+2)

$$-3.2 { \left(x-4 \right) }^{ 2 } (x+2)$$

Evaluate

$$-\frac{16\left(x+2\right)\left(x-4\right)^{2}}{5}$$

Solution Steps

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

$$-3.2\left(x^{2}-8x+16\right)\left(x+2\right)$$

Use the distributive property to multiply -3.2 by x^{2}-8x+16.

$$\left(-3.2x^{2}+25.6x-51.2\right)\left(x+2\right)$$

Use the distributive property to multiply -3.2x^{2}+25.6x-51.2 by x+2 and combine like terms.

$$-3.2x^{3}+19.2x^{2}-102.4$$

Expand

$$\frac{-16x^{3}+96x^{2}-512}{5}$$

Solution Steps

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

$$-3.2\left(x^{2}-8x+16\right)\left(x+2\right)$$

Use the distributive property to multiply -3.2 by x^{2}-8x+16.

$$\left(-3.2x^{2}+25.6x-51.2\right)\left(x+2\right)$$

Use the distributive property to multiply -3.2x^{2}+25.6x-51.2 by x+2 and combine like terms.

$$-3.2x^{3}+19.2x^{2}-102.4$$