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

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

Use the distributive property to multiply -3 by x^{2}-2x+1.

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

Use the distributive property to multiply -3x^{2}+6x-3 by x^{2}-4 and combine like terms.

$$-3x^{4}+9x^{2}+6x^{3}-24x+12$$

Expand

$$12-24x+9x^{2}+6x^{3}-3x^{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

Use the distributive property to multiply -3 by x^{2}-2x+1.

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

Use the distributive property to multiply -3x^{2}+6x-3 by x^{2}-4 and combine like terms.

$$-3x^{4}+9x^{2}+6x^{3}-24x+12$$