Question

question
expand the expression to a polynomial in standard form:
$(3x + 1)(2x^2 + 8x + 7)$

Explanation:

Step1: Distribute $3x$ to each term

$3x \cdot 2x^2 + 3x \cdot 8x + 3x \cdot 7$
$= 6x^3 + 24x^2 + 21x$

Step2: Distribute $1$ to each term

$1 \cdot 2x^2 + 1 \cdot 8x + 1 \cdot 7$
$= 2x^2 + 8x + 7$

Step3: Combine all resulting terms

$6x^3 + 24x^2 + 21x + 2x^2 + 8x + 7$

Step4: Combine like terms

$6x^3 + (24x^2+2x^2) + (21x+8x) + 7$
$= 6x^3 + 26x^2 + 29x + 7$

Answer:

$6x^3 + 26x^2 + 29x + 7$