We want to find the greatest common factor (GCF) of the terms in the given expression. To do so, we will consider coefficients and variables separately.
25 b^2- 20 b
Let's start by finding the GCF of 25 and 20 by listing all possible factors of both numbers.
Factors of25:& 1, 5, and25
Factors of20:& 1,2,4, 5,10, and 20
We found that the GCF of the coefficients is 5. To find the GCF of the variables, we need to identify the all possible variable factors in both terms.
\begin{aligned}
\textbf{Factors of }\bm{1^\textbf{st}}\textbf{ Variable:}&\ {\color{#FF0000}{b}}, b^2\\
\textbf{Factors of }\bm{2^\textbf{nd}}\textbf{ Variable:}&\ {\color{#FF0000}{b}}
\end{aligned}
We see that there is one repeated variable factor, b.
Therefore, the GCF of the expression is 5* b= 5b. Now we can write the given expression in terms of the GCF.
25b^2-20b ⇔ 5b* 5b- 5b* 4
Finally, we will factor out the GCF.
5b* 5b- 5b* 4 ⇔ 5b(5b-4)
Checking Our Answer
Check your answer âś“
To check our answer, we can apply the Distributive Property and compare the result with the given expression.
