Question

How do you simplify 2a – 5(a + 1)?

Answer 1

We will first use the distributive property to simplify the bracket in the given expression, then we will just carry on with the calculations.

Complete step by step answer: We are given that we are required to simplify 2a – 5(a + 1).
We see that we have two terms which are 2a and - 5 (a + 1) which are clubbed using addition.
Now, we by using the distributive property, we will then obtain the following equation with us:-
$\Rightarrow$- 5 (a + 1) = - 5 (a) + (- 5) (1)
Multiplying and simplifying the values on the right hand side, we will then obtain the following equation with us:-
$\Rightarrow$- 5 (a + 1) = - 5a – 5
Now, adding 2a on the both sides of the above equation, we will then obtain the following equation with us:-
$\Rightarrow$ 2a – 5 (a + 1) = 2a - 5a – 5
Now, we see that there are two terms containing a on the right hand side of the above expression, therefore clubbing those terms, we will then obtain the following equation with us:-
$\Rightarrow$ 2a – 5 (a + 1) = - 3a – 5
Hence, the required answer is – 3a – 5.

Note:
We must note the definition of the distributive property we used in the above solution. It is given as follows:-
$\Rightarrow$ a (b + c) = ab + ac, for all the numbers a, b and c.
The students must also note that we actually took out a common in that step, where we clubbed the like terms 2a and – 5a as follows:-
$\Rightarrow$ 2a – 5a = (2 – 5)a
Simplifying the calculations on the right hand side of the above equation, we will then obtain the following equation with us:-
$\Rightarrow$ 2a – 5a = - 3a