How do you factor #7a + 28b#?
To factor the expression, we require to find a factor or factors that are common to both 7a and 28b. This would be a
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
Factors of 28 are
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(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.
#color(blue)"common factor"#of 7a and 28b is therefore 7.
Write 7 followed by an 'open' bracket'
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.