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.
10 a^2+ 40 a
Let's start by finding the GCF of 10 and 40.
Factors of10:& 1,2,5and 10
Factors of40:& 1,2,4,5,8, 10,20and 40
We found that the GCF of the coefficients is 10. To find the GCF of the variables, we need to identify the variables repeated in both terms, and write them with their minimum exponents.
\begin{aligned}
\textbf{Factors of }\bm{1^\text{st}}\textbf{ Variable:}&\ {\color{#FF0000}{a}}, a^2\\
\textbf{Factors of }\bm{2^\text{nd}}\textbf{ Variable:}&\ {\color{#FF0000}{a}}
\end{aligned}
We see that there is one repeated variable factor, a. Therefore, the GCF of the expression is 10* a= 10a. Now we can write the given expression in terms of the GCF.
10a^2+40a ⇔ 10a* a+ 10a* 4
Finally, we will factor out the GCF.
10a* a+ 10a* 4 ⇔ 10a(a+4)
Checking Our Answer
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To check our answer, we can apply the Distributive Property and compare the result with the given expression.
