Question
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Answer
The simplified form is \( 8a^{3}+12a^{2}b+6ab^{2}+b^{3}-1 \).
Solution
Calculate or simplify the expression \( (2a+b)^3-1 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(2a+b\right)^{3}-1\)
- step1: Expand the expression:
\(8a^{3}+12a^{2}b+6ab^{2}+b^{3}-1\)
The simplified form of the expression \( (2a+b)^3-1 \) is \( 8a^{3}+12a^{2}b+6ab^{2}+b^{3}-1 \).
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Simplify this solution The Deep Dive
To expand \( (2a + b)^{3} - 1 \), we can start by recognizing that \( (2a + b)^{3} \) can be applied using the binomial theorem or by multiplying it out step-by-step. After expanding, we get \( 8a^{3} + 12a^{2}b + 6ab^{2} + b^{3} - 1 \). This expression represents a polynomial with respect to variables \( a \) and \( b \). Additionally, this expression can be useful for finding specific values when you plug in different values for \( a \) and \( b \). For instance, if \( a = 1 \) and \( b = 2 \), simply substitute these values into the expanded polynomial to see how it behaves, which can aid both in understanding its properties and in various applications like optimization or graphing!
