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

1 Answer
Jul 23, 2016

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)#