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Chapter 7: Problem 14

Find the greatest common factor of each group of terms. $$ a^{2}(h+8), b^{2}(h+8) $$

Short Answer

Expert verified
The greatest common factor of the expressions \(a^{2}(h+8)\) and \(b^{2}(h+8)\) is \((h+8)\).

Step by step solution

01

Identify the common factors of the expressions

First, we need to list the factors of each term in the given expressions: Factors of \(a^{2}(h+8)\) are: \(a^2\), and \((h+8)\) Factors of \(b^{2}(h+8)\) are: \(b^2\), and \((h+8)\) Now, we need to compare the factors and find the common ones.
02

Determine the common factors

On comparing the factors of the two expressions, we find a common factor: \((h+8)\) There is no other common factor between these two expressions.
03

Find the most significant common factor

As there is only one common factor for the given expressions (\(h+8\)), it is the greatest common factor. Therefore, the greatest common factor of the given expressions \(a^{2}(h+8)\) and \(b^{2}(h+8)\) is \((h+8)\).

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