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(2q^(5)+7q)+(5q^(5)+3q^(3))
Which of the following expressions is equivalent to the given expression?
Choose 1 answer:
(A)
q(7q^(4)+10)
(B)
q(7q^(4)+10q^(2))
(C)
q(2q^(4)+12q^(3)+3q^(2))
(D)
q(7q^(4)+3q^(2)+7)

$\left(2 q^{5}+7 q\right)+\left(5 q^{5}+3 q^{3}\right)$ $\newline$ Which of the following expressions is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $q\left(7 q^{4}+10\right)$ $\newline$ (B) $q\left(7 q^{4}+10 q^{2}\right)$ $\newline$ (C) $q\left(2 q^{4}+12 q^{3}+3 q^{2}\right)$ $\newline$ (D) $q\left(7 q^{4}+3 q^{2}+7\right)$

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Compare linear and exponential growth

Full solution

Q.

\left(2 q^{5}+7 q\right)+\left(5 q^{5}+3 q^{3}\right)

\newline

Which of the following expressions is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

q\left(7 q^{4}+10\right)

\newline

(B)

q\left(7 q^{4}+10 q^{2}\right)

\newline

(C)

q\left(2 q^{4}+12 q^{3}+3 q^{2}\right)

\newline

(D)

q\left(7 q^{4}+3 q^{2}+7\right)

Combine like terms: Combine like terms in the expression $(2q^{5}+7q)+(5q^{5}+3q^{3})$ . $\newline$ To combine like terms, we add the coefficients of the terms with the same exponent. $\newline$ The terms $2q^{5}$ and $5q^{5}$ are like terms, so we add their coefficients: $2 + 5 = 7$ . $\newline$ The term $7q$ has no like term to combine with, so it remains as is. $\newline$ The term $3q^{3}$ has no like term to combine with, so it remains as is. $\newline$ The combined expression is $7q^{5} + 3q^{3} + 7q$ .
Add coefficients of like terms: Look at the answer choices to determine which one matches the combined expression. $\newline$ (A) $q(7q^{4}+10)$ does not match because it does not have a $q^{5}$ term or a $q^{3}$ term. $\newline$ (B) $q(7q^{4}+10q^{2})$ does not match because it does not have a $q^{5}$ term or a $q^{3}$ term. $\newline$ (C) $q(2q^{4}+12q^{3}+3q^{2})$ does not match because the coefficients of $q^{5}$ and $q^{3}$ terms do not match the combined expression. $\newline$ (D) $q(7q^{4}+3q^{2}+7)$ does not match because it does not have a $q^{5}$ term or a $q^{3}$ term, and the factorization is incorrect. $\newline$ None of the answer choices directly match the combined expression $q^{5}$ $2$ .
Identify terms with no like terms: Realize that there is a mistake in the previous step because the combined expression should be correctly matched with one of the answer choices. $\newline$ We need to re-evaluate the answer choices with the correct combined expression $7q^{5} + 3q^{3} + 7q$ .

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