How do you factor 7a + 28b7a+28b?
1 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"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"numeric factors of 7a and 28b Factors of 7 are
1,color(red)(7)1,7 Factors of 28 are
1,2,4,color(red)(7),14,281,2,4,7,14,28 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)7 Consider the
color(magenta)"algebraic factors of 7a and 28b"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"common factor of 7a and 28b is therefore 7.Write 7 followed by an 'open' bracket'
color(red)(7)(7( To obtain the contents of the bracket, think the following.
color(red)(7)xx?=7a" the answer is a"7×?=7a the answer is a
color(red)(7)xx?=28b" the answer is 4b"7×?=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)⇒7a+28b=7(a+4b)
