Question
\( 1 \leftarrow \underbrace{\left(2 a^{3}+4 b^{3}\right)-\left(4 a^{2} b-3 a b^{2}+4 b^{3}+2 a^{3}\right)} \begin{array}{l}\text { The difference is } \square . \text { (Simplify your answer.) } \\ \end{array} \)
Ask by Moreno Coleman. in the United States
Feb 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The difference is \( ab(3b - 4a) \).
Solution
We start with the expression:
(2a³ + 4b³) - (4a²b - 3ab² + 4b³ + 2a³).
Step 1: Distribute the minus sign to the second group:
2a³ + 4b³ - 4a²b + 3ab² - 4b³ - 2a³.
Step 2: Combine like terms:
2a³ - 2a³ = 0,
4b³ - 4b³ = 0,
leaving us with:
-4a²b + 3ab².
Step 3: Factor out the common factor ab:
ab(-4a + 3b).
Thus, the simplified expression is: ab(3b - 4a).
The difference is ab(3b - 4a).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To simplify the expression, we first need to combine all the terms: \[ (2a^3 + 4b^3) - (4a^2b - 3ab^2 + 4b^3 + 2a^3) \] Distributing the negative sign: \[ 2a^3 + 4b^3 - 4a^2b + 3ab^2 - 4b^3 - 2a^3 \] Now, we can combine the like terms. The \(2a^3\) and \(-2a^3\) cancel out, and the \(4b^3\) and \(-4b^3\) also cancel: \[ -4a^2b + 3ab^2 \] Thus, the simplified expression is: \[ 3ab^2 - 4a^2b \] So, the difference is \(3ab^2 - 4a^2b\).
