Question

How do you simplify \[ - (r + s) - (2r + 2s)\]?

Answer 1

Hint: We are given a mathematical equation that is a combination of both numerical values and alphabets, such types of mathematical equations are called algebraic expressions. Generally the variables are denoted by alphabets. Here we have two unknown variables. One is ‘r’ and the other is ‘s’. We regroup this and simplify, we will get the required result.

Complete step-by-step answer:
Given, \[ - (r + s) - (2r + 2s)\]
Let’s take the first brackets terms, that is \[ - (r + s)\]. The meaning of this is negative one is multiplied to both ‘r’ and ‘s’. That is
\[ - (r + s) = - 1 \times (r + s)\]
We know that multiplication of a positive and a negative number or variable gives us a negative number or variable.
\[ - (r + s) = - r - s\].
Applying same concept for the second bracket terms we have,
\[ - (2r + 2s) = - 2r - 2s\].
This the given problem becomes,
\[ - (r + s) - (2r + 2s) = - r - s - 2r - 2s\]
In the right hand side of the equation we need to group ‘s’ terms and ‘r’ terms. We have,
\[ = - r - 2r - 2s - s\]
Taking \[ - r\]common in the first two terms and taking \[ - s\]common in the remaining two terms we have,
\[ = - r(1 + 2) - s(2 + 1)\]
\[ = - 3r - 3s\]
Taking \[ - 3\] common we have,
\[ = - 3(r + s)\].
Hence the simplified form of \[ - (r + s) - (2r + 2s)\] is \[ - 3(r + s)\].
So, the correct answer is “\[ - 3(r + s)\]”.

Note: Careful in the calculation part. We can find the value of a given expression if we know the value of ‘r’ and ‘s’. Algebra helps in converting a mathematical statement or word problem into an equation. After converting into an equation we solve that easily. Careful in the sign changing and know the sign multiplication of two numbers. That is, the product of two negative numbers will give positive number, product of negative and positive number will give negative number.