Solve f(x)=4(x+5)(x-3)^2

$$f ( x ) = 4 ( x + 5 ) ( x - 3 ) ^ { 2 }$$

Evaluate

$$4\left(x+5\right)\left(x-3\right)^{2}$$

Solution Steps

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

$$4\left(x+5\right)\left(x^{2}-6x+9\right)$$

Use the distributive property to multiply 4 by x+5.

$$\left(4x+20\right)\left(x^{2}-6x+9\right)$$

Use the distributive property to multiply 4x+20 by x^{2}-6x+9 and combine like terms.

$$4x^{3}-4x^{2}-84x+180$$

Expand

$$4x^{3}-4x^{2}-84x+180$$

Solution Steps

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

$$4\left(x+5\right)\left(x^{2}-6x+9\right)$$

Use the distributive property to multiply 4 by x+5.

$$\left(4x+20\right)\left(x^{2}-6x+9\right)$$

Use the distributive property to multiply 4x+20 by x^{2}-6x+9 and combine like terms.

$$4x^{3}-4x^{2}-84x+180$$