Question

How do you factor the expression $6a+6b$ ?

Answer 1

Hint: we are asked to factor the form of the expression $6a+6b$. To find the solution first we know about what the factor form of the equation means. Then we start working on these with the example. We can also cross check our answer by again expanding our product form. If it matches then we are getting the correct solution.

Complete step-by-step solution:
We are given $6a+6b$. We have to find the factor of it. Before we find this we need to know what does it mean, what does factor mean.
Factor of any term means the possible term which can divide the given term. For example: say we have ‘4’ so ‘4’ is divided by 1,2 and 4 as well.
So, 1, 2 and 4 are known as factors of ‘4’.
If we have more than one term then to find the factor of those then we have to look for those values which divide each of the given terms of the equation.
When we find a factor we then expand the term into its least possible factor.
Like, we have $4{{x}^{2}}$
Then we can see that –
$4{{x}^{2}}$ is divisible by $2,1,4,x\text{ and }{{x}^{2}}$
So factor of $4{{x}^{2}}$ is $1,2,4,x,{{x}^{2}},2{{x}^{2}},2x,4{{x}^{2}}$
Now we have learned that when we have to find the factor of an equation containing multiple terms then we factor each term and take the common term in $6a+6b$ we have 2 terms 6a and 6b.
Factor of 6a are
$6a=2\times 3\times a$
And factor of 6b are
$6b=2\times 3\times b$
Now,
$6a+6b=2\times 3\times a+2\times 3\times b$
As $2\times 3$ is same so take it out as common, so we get –
$\begin{align}
  & =2\times 3\left( a+b \right) \\
 & =6\left( a+b \right) \\
\end{align}$
So factor form of $6a+6b$ is $6\left( a+b \right)$

Note: Now when we get our solution we can always recheck our answer just to be sure that what we have done is correct or not.
Now, we get –
$6a + 6b = 6\left(a+b \right)$
We will solve the right side and check if it is the same as the left side or not.
Now
$\begin{align}
  & 6\left( a+b \right)=6\times a+6\times b \\
 & =6a+6b \\
\end{align}$
So,
Right side = left side
Hence, the solution is correct.