Question

simplify the expression ((x + 4)(x^2 - 4x + 2))

Explanation:

Step1: Use the distributive property (FOIL for binomial and trinomial)

Multiply \(x\) by each term in \((x^{2}-4x + 2)\) and \(4\) by each term in \((x^{2}-4x + 2)\):
\(x(x^{2}-4x + 2)+4(x^{2}-4x + 2)\)

Step2: Distribute \(x\) and \(4\)

For \(x(x^{2}-4x + 2)\): \(x\times x^{2}-x\times4x+x\times2=x^{3}-4x^{2}+2x\)
For \(4(x^{2}-4x + 2)\): \(4\times x^{2}-4\times4x + 4\times2 = 4x^{2}-16x + 8\)

Step3: Combine like terms

Add the two results together: \((x^{3}-4x^{2}+2x)+(4x^{2}-16x + 8)\)
Combine like terms \(-4x^{2}+4x^{2}=0\) and \(2x-16x=-14x\)
So we get \(x^{3}-14x + 8\)

Answer:

\(x^{3}-14x + 8\)