Question

Simplify combining like terms $21b - 32 + 7b - 20b$ .

Answer 1

Hint: The expression given in the question is an algebraic expression. It is a simple algebraic simple expression. To solve an algebraic expression we first check brackets and parentheses. Though in this question we don’t need that primary step as the question involves simple summing of like terms. First we notice the like terms and combine them together. Later as per the actions (addition or subtraction) we simplify them. Lastly, we combine constants.

Complete step-by-step solution:
The like terms in the expression $21b - 32 + 7b - 20b$ are 21b, 7b, 20b.
$21b - 32 + 7b - 20b \\
= 21b + 7b - 20b - 32 \\
= 28b - 20b - 32 \\
= 8b - 32 $
So the simplified form of expression $21b - 32 + 7b - 20b$ is $8b - 32$ .
Here as the expression is simple we completed in a few steps but in many cases expressions need not be this simple. For example let’s consider an example $4{x^2} + 3x - {x^{^2}} - 6(x - 1)$ .
1. First we simplify the terms involving brackets by letting the multiplying factor into it.
2. Next we gather the like terms and simplify the expression.
3. Lastly we combine the constant terms.
The like terms here in this expression are ( $4{x^2}$, ${x^{^2}}$ ) , ($3x$ , $x$) and the constant is 6(-1) .
$ 4{x^2} + 3x - {x^{^2}} - 6(x - 1) \\
= 4{x^2} + 3x - {x^{^2}} - (6x - 6) \\
= 4{x^2} + 3x - {x^{^2}} - 6x + 6 \\
= 4{x^2} - {x^{^2}} + 3x - 6x + 6 \\
= 3{x^{^2}} + 3x - 6x + 6 \\
= 3{x^{^2}} - 3x + 6 \\
$
By simplifying the expression $4{x^2} + 3x - {x^{^2}} - 6(x - 1)$ we get $3{x^{^2}} - 3x + 6$.

Note: The above mentioned way is the way to be followed in case of algebraic expressions . Like terms are terms containing the same degree of coefficient and the degree of coefficient of constant term is 0 .We can only add like terms.Unlike terms can’t be summed up, that is we cannot combine x2 and x terms.