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Answer
The expression \(27+8x^3\) factors to \((3+2x)(9-6x+4x^{2})\).
Solution
Factor the expression \( 27+8x^3 \).
Factor the expression by following steps:
- step0: Factor:
\(27+8x^{3}\)
- step1: Rewrite the expression:
\(3^{3}+\left(2x\right)^{3}\)
- step2: Factor the expression:
\(\left(3+2x\right)\left(3^{2}-3\times 2x+\left(2x\right)^{2}\right)\)
- step3: Evaluate:
\(\left(3+2x\right)\left(9-6x+4x^{2}\right)\)
The factored form of the expression \(27+8x^3\) is \((3+2x)(9-6x+4x^{2})\).
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Simplify this solution Mind Expander
To factor \( 27 + 8x^3 \), we can recognize it as a sum of cubes. Specifically, \( 27 = 3^3 \) and \( 8x^3 = (2x)^3 \). The sum of cubes formula is \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \). Here, let \( a = 3 \) and \( b = 2x \). Applying the formula: \[ 27 + 8x^3 = (3 + 2x)((3)^2 - (3)(2x) + (2x)^2) = (3 + 2x)(9 - 6x + 4x^2). \] Thus, the factored form is: \[ \boxed{(3 + 2x)(9 - 6x + 4x^2)}. \]
