Question

How do you simplify $ 4a + 5{a^2} + 2{a^2} + {a^2} $ ?

Answer 1

Hint: Since the given expression is an algebraic expression, the process of solving the addition will be a little different. For the additional part the terms with the same power are to be added and the remaining terms are to be kept as it is. At the last step you can remove the common terms outside the bracket if there are any.

Complete step-by-step answer:
we have to simplify the above given algebraic expression.
All we have given to do is simple addition. But since it’s an algebraic expression, the addition becomes a little different. While solving this type of algebraic expression, one of the rules while adding is we can only add the terms whose powers are the same irrespective of the coefficient.
Also even if the powers are the same and variables are not the same, we cannot add them.
So in short, terms having the same power and same variables irrespective of their coefficients can be added together.
Hence the above expression will become
 $ 4a + 5{a^2} + 2{a^2} + {a^2} $ $ = 4a + \left( {5{a^2} + 2{a^2} + {a^2}} \right) $
Adding all the like terms we get
 $ = 4a + 8{a^2} $
Now further we can continue with the process of factorization. i.e. we can take the terms which are common in both the terms outside the bracket. So the above expression becomes
 $ = 4a\left( {1 + 2a} \right) $
Now the above expression cannot be simplified further.
So, the correct answer is “ $ = 4a\left( {1 + 2a} \right) $ ”.

Note: The same process is to be followed for subtraction as well. But the only difference is the will of signs. They make a great difference. Also the rules for multiplication and division in algebraic expressions also differ a bit. The part where brackets are included in the expressions also change the meaning of the expression.