Solve f(x)=-4(x-2)^2(x^2-9)

$$f ( x ) = - 4 ( x - 2 ) ^ { 2 } ( x ^ { 2 } - 9 )$$

Evaluate

$$-4\left(x-2\right)^{2}\left(x^{2}-9\right)$$

Solution Steps

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

$$-4\left(x^{2}-4x+4\right)\left(x^{2}-9\right)$$

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

$$\left(-4x^{2}+16x-16\right)\left(x^{2}-9\right)$$

Use the distributive property to multiply -4x^{2}+16x-16 by x^{2}-9 and combine like terms.

$$-4x^{4}+20x^{2}+16x^{3}-144x+144$$

Expand

$$144-144x+20x^{2}+16x^{3}-4x^{4}$$

Solution Steps

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

$$-4\left(x^{2}-4x+4\right)\left(x^{2}-9\right)$$

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

$$\left(-4x^{2}+16x-16\right)\left(x^{2}-9\right)$$

Use the distributive property to multiply -4x^{2}+16x-16 by x^{2}-9 and combine like terms.

$$-4x^{4}+20x^{2}+16x^{3}-144x+144$$