Solve t(x)=-2x^4(x+2)^3(x-1)

$$t ( x ) = - 2 x ^ { 4 } ( x + 2 ) ^ { 3 } ( x - 1 )$$

Evaluate

$$-2\left(x-1\right)\left(x+2\right)^{3}x^{4}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+2\right)^{3}.

$$-2x^{4}\left(x^{3}+6x^{2}+12x+8\right)\left(x-1\right)$$

Use the distributive property to multiply -2x^{4} by x^{3}+6x^{2}+12x+8.

$$\left(-2x^{7}-12x^{6}-24x^{5}-16x^{4}\right)\left(x-1\right)$$

Use the distributive property to multiply -2x^{7}-12x^{6}-24x^{5}-16x^{4} by x-1 and combine like terms.

$$-2x^{8}-10x^{7}-12x^{6}+8x^{5}+16x^{4}$$

Expand

$$16x^{4}+8x^{5}-12x^{6}-10x^{7}-2x^{8}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+2\right)^{3}.

$$-2x^{4}\left(x^{3}+6x^{2}+12x+8\right)\left(x-1\right)$$

Use the distributive property to multiply -2x^{4} by x^{3}+6x^{2}+12x+8.

$$\left(-2x^{7}-12x^{6}-24x^{5}-16x^{4}\right)\left(x-1\right)$$

Use the distributive property to multiply -2x^{7}-12x^{6}-24x^{5}-16x^{4} by x-1 and combine like terms.

$$-2x^{8}-10x^{7}-12x^{6}+8x^{5}+16x^{4}$$