Question

expand the expression to a polynomial in standard form:
$(x - 4)(3x^2 - 6x + 4)$

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \( x \) by each term in \( 3x^2 - 6x + 4 \) and \( -4 \) by each term in \( 3x^2 - 6x + 4 \):
\( x(3x^2 - 6x + 4) - 4(3x^2 - 6x + 4) \)
\( = 3x^3 - 6x^2 + 4x - 12x^2 + 24x - 16 \)

Step2: Combine like terms

Combine the \( x^2 \) terms and the \( x \) terms:
\( 3x^3 + (-6x^2 - 12x^2) + (4x + 24x) - 16 \)
\( = 3x^3 - 18x^2 + 28x - 16 \)

Answer:

\( 3x^3 - 18x^2 + 28x - 16 \)