Question

expand the expression to a polynomial in standard form: (2x - 7)(2x² + 4x + 3)

Explanation:

Step1: Apply the distributive property (FOIL for polynomials)

Multiply \(2x\) by each term in \((2x^{2}+4x + 3)\) and \(-7\) by each term in \((2x^{2}+4x + 3)\):
\(2x\times(2x^{2}+4x + 3)=2x\times2x^{2}+2x\times4x+2x\times3 = 4x^{3}+8x^{2}+6x\)
\(-7\times(2x^{2}+4x + 3)=-7\times2x^{2}-7\times4x-7\times3=-14x^{2}-28x - 21\)

Step2: Combine like terms

Add the two results together:
\((4x^{3}+8x^{2}+6x)+(-14x^{2}-28x - 21)=4x^{3}+(8x^{2}-14x^{2})+(6x - 28x)-21\)
Simplify each like - term group:
\(8x^{2}-14x^{2}=-6x^{2}\)
\(6x - 28x=-22x\)
So the expanded form is \(4x^{3}-6x^{2}-22x - 21\)

Answer:

$4x^{3}-6x^{2}-22x - 21$