Problem 14 - Beginning and Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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 \((h+8)\).