How do you factor 7a + 28b?

Jul 23, 2016

7(a +4b)

Explanation:

To factor the expression, we require to find a factor or factors that are common to both 7a and 28b. This would be a $\textcolor{b l u e}{\text{common factor}}$

The factors of a number are those numbers which divide exactly into the given number with no remainder.

For example, the factors of 12 are 1,2.3.4,6 and 12.

Now consider the $\textcolor{m a \ge n t a}{\text{numeric factors of 7a and 28b}}$

Factors of 7 are $1 , \textcolor{red}{7}$

Factors of 28 are $1 , 2 , 4 , \textcolor{red}{7} , 14 , 28$

When considering the common factor, look for the lowest and exclude 1 as this would leave the expression unchanged.

Lowest common factor of 7 and 28 is$\textcolor{red}{7}$

Consider the $\textcolor{m a \ge n t a}{\text{algebraic factors of 7a and 28b}}$

Factors of a are 1 , a

Factors of b are 1 , b

Since 1 is excluded there are no common factors between a and b.

The $\textcolor{b l u e}{\text{common factor}}$ of 7a and 28b is therefore 7.

Write 7 followed by an 'open' bracket'

color(red)(7)(

To obtain the contents of the bracket, think the following.

color(red)(7)xx?=7a" the answer is a"

color(red)(7)xx?=28b" the answer is 4b"

a and 4b are placed inside the bracket with the appropriate + sign between them.
Finally close the bracket.

$\Rightarrow 7 a + 28 b = 7 \left(a + 4 b\right)$