Question

How do you simplify: 7a +3b – 4a – 5b?

Answer 1

Hint: Assume the given expression as ‘E’. Now, group the terms containing the variable ‘a’ together while group the terms containing the variable ‘b’ together. Take ‘a’ common from the terms containing ‘a’ and ‘b’ common from the terms containing ‘b’, use simple arithmetic operations: addition or subtraction, whichever needed, to simplify the expression.

Complete step by step solution:
Here, we have been provided with the expression: 7a +3b – 4a – 5b and we are asked to simplify it.
Now, let us assume the given expression as E, so we have,
$\Rightarrow $ E = 7a +3b – 4a – 5b
In the above expression we can see that there are four terms in which two of them contain the variable ‘a’ and two of them contain the variable ‘b’, so we have to group the terms containing the variable ‘a’ together and the terms containing the variable ‘b’ together to simplify them. So, we have on grouping,
$\Rightarrow $ E = (7a – 4a) + (3b – 5b)
Taking ‘a’ common from the first two terms in the bracket and ‘b’ common from the last two terms in bracket, we get,
$\Rightarrow $ E = a (7 – 4) + b (3 – 5)
Therefore, on simplifying we get,
$\Rightarrow $ E = 3a – 2b
Hence, the simplified value of the given expression is: 3a – 2b which is our answer.

Note: One may consider ‘a’ and ‘b’ as the constants or variables that do not matter here. Note that actually there are not four terms but only two terms here. One is a term containing the variable ‘a’ and the other is the term containing the variable ‘b’. Sometimes you may be asked how many terms are there in the given expression, so in such cases first you need to simplify the expression and then conclude the answer otherwise the answer may be considered incorrect.