Question

expand the expression to a polynomial in standard form:
$(2x - 7)(2x^2 + 4x + 3)$

Explanation:

Step1: Use distributive property (FOIL for polynomials)

Multiply \(2x\) with each term in \(2x^2 + 4x + 3\) and \(-7\) with each term in \(2x^2 + 4x + 3\).
\(2x(2x^2)+2x(4x)+2x(3)-7(2x^2)-7(4x)-7(3)\)

Step2: Simplify each term

\(4x^3 + 8x^2 + 6x - 14x^2 - 28x - 21\)

Step3: Combine like terms

Combine the \(x^2\) terms and \(x\) terms.
\(4x^3+(8x^2 - 14x^2)+(6x - 28x)-21\)
\(4x^3 - 6x^2 - 22x - 21\)

Answer:

\(4x^3 - 6x^2 - 22x - 21\)