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

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

Evaluate

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

Solution Steps

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

$$-3x\left(x+1\right)\left(x^{2}-8x+16\right)$$

Use the distributive property to multiply -3x by x+1.

$$\left(-3x^{2}-3x\right)\left(x^{2}-8x+16\right)$$

Use the distributive property to multiply -3x^{2}-3x by x^{2}-8x+16 and combine like terms.

$$-3x^{4}+21x^{3}-24x^{2}-48x$$

Expand

$$-3x^{4}+21x^{3}-24x^{2}-48x$$

Solution Steps

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

$$-3x\left(x+1\right)\left(x^{2}-8x+16\right)$$

Use the distributive property to multiply -3x by x+1.

$$\left(-3x^{2}-3x\right)\left(x^{2}-8x+16\right)$$

Use the distributive property to multiply -3x^{2}-3x by x^{2}-8x+16 and combine like terms.

$$-3x^{4}+21x^{3}-24x^{2}-48x$$