Question

Expand the following and collect like terms:
$\left( a \right)\left( {x + 5} \right)\left( {x + 5} \right)$
$\left( b \right)\left( {x + 9} \right)\left( {x + 9} \right)$

Answer 1

Hint: In this question we have been given two terms that are being told to expand them and then collect the like terms. Expand means that we need to simplify by multiplying the bracket quantities, collecting like terms means we have to add up or subtract how so ever it is the terms which are exactly similar that are having the same variable power.

Complete step-by-step answer:

$\left( a \right)\left( {x + 5} \right)\left( {x + 5} \right)$
We have to expand this equation and collect like terms so first expand it we have,
$ \Rightarrow \left( {x + 5} \right)\left( {x + 5} \right) = {x^2} + 5x + 5x + 25$
So in above equation 5x and 5x are like terms so collect them and make as a single term we have,
$ \Rightarrow \left( {x + 5} \right)\left( {x + 5} \right) = {x^2} + \left( {5 + 5} \right)x + 25 = {x^2} + 10x + 25$
So this is the required expansion.

$\left( b \right)\left( {x + 9} \right)\left( {x + 9} \right)$
We have to expand this equation and collect like terms so first expand it we have,
$ \Rightarrow \left( {x + 9} \right)\left( {x + 9} \right) = {x^2} + 9x + 9x + 81$
So in above equation 9x and 9x are like terms so collect them and make as a single term we have,
$ \Rightarrow \left( {x + 9} \right)\left( {x + 9} \right) = {x^2} + \left( {9 + 9} \right)x + 81 = {x^2} + 18x + 81$

So this is the required expansion.

Note: Whenever we face such types of problems the key concept is simply to multiply the bracket terms carefully, always look for the coefficients of the same variable power. This helps us in deciding whether the terms are like terms or not. Use this concept to get on the right track to get the answer.