Question
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Answer
\( b^{3} - 12b^{2} + b \)
Solution
1. Distribute \( b \) to each term inside the parentheses:
\[
b\left(b^{2}-12b+1\right)=b\cdot b^{2}-12b\cdot b+b\cdot 1.
\]
2. Simplify each term:
\[
b\cdot b^{2}=b^{3},\quad -12b\cdot b=-12b^{2},\quad b\cdot 1=b.
\]
3. Combine the simplified terms:
\[
b^{3}-12b^{2}+b.
\]
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Simplify this solution Mind Expander
To factor the expression \( b(b^2 - 12b + 1) \), first identify the quadratic part \( b^2 - 12b + 1 \). This can be analyzed using the quadratic formula \( b = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A} \), where \( A=1, B=-12, \) and \( C=1 \). Plugging in these values gives the roots of the quadratic, which can help in further simplifying the expression based on its factors. Additionally, while working with polynomials, a common mistake is forgetting to distribute properly or miscalculating the discriminant in the quadratic formula. Always double-check your calculations for accuracy and try to factor quadratics, if possible, before further computations!
