Question

Simplify the following expression: $21b-60+7b-20b$

Answer 1

Hint: For this question, we will analyze the given algebraic expression and then we will look for any brackets, if they are not there we will then look for the like terms and we will combine them. This means terms with the same variables are put together and then are solved. Finally take the common variable or consonant out of the expression and solve the rest of the expression to get the simpler term.

Complete step by step answer:
First we will see what exactly is simplifying. So whenever we are given an algebraic expression we need to reduce it into a simpler form. This will help us in making our calculations much easier. So to simplify an algebraic expression: we need to follow the following steps:
A. First remove the parentheses by multiplying factors into the bracket
B. Then use exponent rules to remove parentheses in terms with exponents
C. After that combine like terms by adding coefficients
D. Finally, combine the constants
Let’s take an example: $5\left( 2+x \right)+3\left( 5x+4 \right)-\left( {{x}^{2}} \right)$ , the first thing to look for is whether you can clear any parentheses. We can use the distributive property to clear parentheses, by multiplying the factors times the terms inside the parentheses. In this expression, we can use the distributive property to get rid of the first two sets of parentheses. Therefore, we will get the following: $10+5x+15x+12-{{x}^{2}}$ , The next step in simplifying is to look for terms and combine them. The terms $5x$ and $15x$ are like terms, because they have the same variable raised to the same power we can add these two terms to get $20x$, the expression will now look like: $10+20x+12-{{x}^{2}}$ . Finally we will see for any constants that we can add, here we see 10 and 22 therefore the expression will now look like: $22+20x-{{x}^{2}}\text{ }......\text{ Equation 1}\text{.}$ now the expression is simplified.
We will now take the given expression in the question: $21b-60+7b-20b$
Let’s first bring the like terms together, that is terms with the variable $b$ : $21b+7b-20b-60$
Now take the common variable out , after that we will get: $b\left( 21+7-20 \right)-60$
Now we will solve the terms inside the bracket and get the simplified form of the expression, that is:
$b\left( 8 \right)-60\Rightarrow 8b-60$

Hence, the answer is: $8b-60$

Note: Usually we write an algebraic expression in a certain order. We start with the terms that have the largest exponents and work our way down to the constants. Using the commutative property of addition, we can rearrange the terms and put the expression in correct order. For example in equation 1 above , we can rearrange it and write as : ${{x}^{2}}-20x-22$ .