Question

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

Answer 1

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)`