Pregunta
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\( b^{3}+216 = (b+6)(b^{2}-6b+36) \)
Solución
Factor the expression \( b^{3}+216 \).
Factor the expression by following steps:
- step0: Factor:
\(b^{3}+216\)
- step1: Rewrite the expression:
\(b^{3}+6^{3}\)
- step2: Factor the expression:
\(\left(b+6\right)\left(b^{2}-b\times 6+6^{2}\right)\)
- step3: Reorder the terms:
\(\left(b+6\right)\left(b^{2}-6b+36\right)\)
The factored form of \(b^{3}+216\) is \((b+6)(b^{2}-6b+36)\).
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Simplifique esta solución Bonus Knowledge
To factor \( b^3 + 216 \), we first recognize that \( 216 \) can be expressed as \( 6^3 \). Thus, we can rewrite the expression as \( b^3 + 6^3 \). This is a sum of cubes, which can be factored using the formula \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \). In this case, set \( a = b \) and \( b = 6 \). Therefore, we have: \[ b^3 + 6^3 = (b + 6)(b^2 - 6b + 36) \] So the factored form of \( b^3 + 216 \) is: \[ (b + 6)(b^2 - 6b + 36) \]
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