Question

1. if $a = 4x^3 + 2x^2 + 3$ and $b = 5x^3 + 3x^2 + x$, which polynomial is equivalent to $3(a + b)$?

a. $-3x^3 - 3x^2 - 3x + 9$
b. $9x^3 + 5x^2 + x + 3$
c. $60x^3 + 18x^2 + 3x + 9$
d. $27x^3 + 15x^2 + 3x + 9$

Explanation:

Step1: Find sum \(a + b\)

Combine like terms of \(a\) and \(b\):

$$\begin{align*} a + b&=(4x^3 + 2x^2 + 3)+(5x^3 + 3x^2 + x)\\ &=(4x^3+5x^3)+(2x^2+3x^2)+x+3\\ &=9x^3 + 5x^2 + x + 3 \end{align*}$$

Step2: Multiply sum by 3

Distribute 3 to each term:

$$\begin{align*} 3(a + b)&=3(9x^3 + 5x^2 + x + 3)\\ &=3\times9x^3 + 3\times5x^2 + 3\times x + 3\times3\\ &=27x^3 + 15x^2 + 3x + 9 \end{align*}$$

Answer:

D. \(27x^3 + 15x^2 + 3x + 9\)