Terms are added or subtracted
to form an
Answers
Answer:
Addition and Subtraction of Monomials
Step-by-step explanation:
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Answer:
Addition and Subtraction of Algebraic Expressions
addition subtraction algebra
Before we see how to add and subtract integers, we define terms and factors.
Terms and Factors
A term in an algebraic expression is an expression involving letters and/or numbers (called factors), multiplied together.
Example 1
The algebraic expression
5x
is an example of one single term. It has factors 5 and x.
The 5 is called the coefficient of the term and the x is a variable.
Example 2
5x + 3y has two terms.
First term: 5x, has factors \displaystyle{5}5 and x
Second term: 3y, has factors \displaystyle{3}3 and y
The \displaystyle{5}5 and \displaystyle{3}3 are called the coefficients of the terms.
Example 3
The expression
\displaystyle{3}{x}^{2}-{7}{a}{b}+{2}{e}\sqrt{{\pi}}3x
2
−7ab+2e
π
has three terms.
First term: \displaystyle{3}{x}^{2}3x
2
has factors \displaystyle{3}3 and x2
Second term: \displaystyle-{7}{a}{b}−7ab has factors \displaystyle-{7}−7, a and b
Third Term: \displaystyle{2}{e}\sqrt{{\pi}}2e
π
; has factors \displaystyle{2}2, \displaystyle{e}e, and \displaystyle\sqrt{{\pi}}
π
.
The \displaystyle{3}3, \displaystyle-{7}−7 and \displaystyle{2}2 are called coefficients of the terms.
Like Terms
"Like terms" are terms that contain the same variables raised to the same power.
Example 4
3x2 and 7x2 are like terms.
Example 5
-8x2 and 5y2 are not like terms, because the variable is not the same.
Adding and Subtracting Terms
Important: We can only add or subtract like terms.
Why? Think of it like this. On a table we have 4 pencils and 2 books. We cannot add the 4 pencils to the 2 books - they are not the same kind of object.
We go get another 3 pencils and 6 books. Altogether we now have 7 pencils and 8 books. We can't combine these quantities, since they are different types of objects.
Next, our sister comes in and grabs 5 pencils. We are left with 2 pencils and we still have the 8 books.
Similarly with algebra, we can only add (or subtract) similar "objects", or those with the same letter raised to the same power.
Example 6
Simplify 13x + 7y − 2x + 6a
Answer
Example 7
Simplify −5[−2(m − 3n) + 4n]
Answer
Note:
The fancy name for round brackets ( ) is "parentheses".
The fancy name for square brackets [ ] is "box brackets".
The fancy name for curly brackets { } is "braces".
Example 8
Simplify −[7(a − 2b) − 4b]
Step-by-step explanation: