Question

How do you factor \[21a-49b-7c\]?

Answer 1

Hint: In this problem, we have to find the factor for the given expression. We can see that the expression contains a common factor 7. We can take the common factor 7 outside the expression and write the remaining terms inside the brackets as a factor. We should also be clear that the factor which we have taken outside must be correct as we multiply it inside, we should get the given expression. We will get the required factor for the expression.

Complete step by step solution:
We know that the expression given is,
 \[21a-49b-7c\]
We can see that the expression contains a common factor 7.
We can take the common factor 7 outside the expression and write the remaining terms inside the brackets as a factor.
We can split the term as,
\[\begin{align}
  & \Rightarrow 7\times 3a=21a \\
 & \Rightarrow 7\times 7b=49b \\
 & \Rightarrow 7\times 1c=7c \\
\end{align}\]
We can write the given expression as by taking the common term 7 outside the expression to get the factor, we get
\[\Rightarrow 7\left( 3a-7b-c \right)\]

Therefore, the required factor is \[7\left( 3a-7b-c \right)\].

Note: We should also be cleared that the factor which we have taken outside must be correct as we multiply it inside, we should get the given expression. We can also multiply the factor to check for the correct answer. If the multiplied answer is not the given expression, then the factor is not a correct one.
\[\begin{align}
  & \Rightarrow 7\times \left( 3a-7b-c \right) \\
 & \Rightarrow 7\times 3a-7\times 7b-7\times c \\
 & \Rightarrow 21a-49b-7c \\
\end{align}\]
Therefore, the factor that we got in the result is correct.