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Chapter 10: Problem 68

Factor. $$18 a^{3}+24 a^{2}+8 a$$

Short Answer

Expert verified
The factored form of the given expression is \(2a(3a+2)^{2}\).

Step by step solution

01

Identify Common Factors

Find the greatest common factor (GCF) that each term of the polynomial shares. In this case, the GCF of \(18a^{3}\), \(24a^{2}\), and \(8a\) is \(2a\).
02

Factor out the GCF

Subtract the power of the GCF from the power of each term in the polynomial to simplify it. This results in the expression \(2a(9a^{2}+12a+4)\).
03

Factor the Remaining Expression

Now, factor the remaining quadratic polynomial. To do this, look for two numbers that multiply to \(9*4\) (or 36) and add up to 12. Two such numbers are 6 and 6. Hence, it further simplifies to \(2a(3a+2)^{2}.\)

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