Question
Simplify. \( 9 x^{5}+8\left(4 x^{5}-6 b^{3}\right) \)
Ask by Kirk Ford. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( 41x^{5} - 48b^{3} \).
Solution
To simplify the expression 9x⁵ + 8(4x⁵ - 6b³), first distribute the 8 into the parentheses:
8(4x⁵ - 6b³) = 32x⁵ - 48b³
Now, add this to the original 9x⁵:
9x⁵ + 32x⁵ - 48b³ = 41x⁵ - 48b³
So the simplified expression is 41x⁵ - 48b³.
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Simplify this solution The Deep Dive
To simplify the expression \( 9 x^{5}+8\left(4 x^{5}-6 b^{3}\right) \), let's start by distributing the 8 across the terms inside the parentheses: \[ 9 x^{5} + 8 \cdot 4 x^{5} - 8 \cdot 6 b^{3} \] This gives us: \[ 9 x^{5} + 32 x^{5} - 48 b^{3} \] Now, combine the like terms \(9 x^{5}\) and \(32 x^{5}\): \[ (9 + 32)x^{5} - 48 b^{3} = 41 x^{5} - 48 b^{3} \] So, the simplified form of the expression is: \[ 41 x^{5} - 48 b^{3} \]
