# How do you factor #7a + 28b#?

##### 1 Answer

#### Answer:

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

#color(blue)"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

#color(magenta)"numeric factors of 7a and 28b"# Factors of 7 are

#1,color(red)(7)# Factors of 28 are

#1,2,4,color(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

#color(red) (7)# Consider the

#color(magenta)"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

#color(blue)"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.

#rArr7a+28b=7(a+4b)#