Question
\( B=p+5 \) and \( A=p^{2}+10 p+1 \), find an expression that equals \( 2 B+3 A \) in standard form
Ask by Cook Gonzalez. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2B + 3A = 3p^{2} + 32p + 13 \)
Solution
To find an expression for \( 2B + 3A \) in standard form, follow these steps:
Given:
\[
B = p + 5
\]
\[
A = p^2 + 10p + 1
\]
Calculate \( 2B + 3A \):
\[
2B + 3A = 2(p + 5) + 3(p^2 + 10p + 1)
\]
\[
= 2p + 10 + 3p^2 + 30p + 3
\]
\[
= 3p^2 + (2p + 30p) + (10 + 3)
\]
\[
= 3p^2 + 32p + 13
\]
**Final Answer:**
\[
2B + 3A = 3\,p^{2} + 32\,p + 13
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Let's start by substituting the expression for \( B \) into \( 2B \): \[ 2B = 2(p + 5) = 2p + 10 \] Next, we'll expand the expression for \( A \): \[ 3A = 3(p^2 + 10p + 1) = 3p^2 + 30p + 3 \] Now we can combine \( 2B \) and \( 3A \): \[ 2B + 3A = (2p + 10) + (3p^2 + 30p + 3) \] Combining like terms, we get: \[ 2B + 3A = 3p^2 + (2p + 30p) + (10 + 3) = 3p^2 + 32p + 13 \] Thus, the expression that equals \( 2B + 3A \) in standard form is: \[ \boxed{3p^2 + 32p + 13} \]
