# Math

How do I identify coefficients, constant terms, and like terms of the expression?

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1. TERMS
Consider the expression:
15x + 9ab - 8 - 10ab + 5a + x - b

A term can be a number, a variable (letter) or the product of a number and variable(s).

Terms can be positive or negative.
The sign of the term is determined by the operation directly in front of the term.

A term is positive(+) if it has no sign and it is the first term in the expression.
A term is positive(+) if the preceding operation is addition.
A term is negative(-) if the preceding operation is subtraction.

In the expression above, the terms are:
15x, 9ab, -8, -10ab, 5a, x, -b

15x is a product of a number and a variable
9ab is a product of a number and two variables
-8 is a number
-10ab is a product of a number and two variables
5a is product of a number and a variable
x is a variable
-b is a variable

Note:
15x is a positive term, because it has no sign and it is the first term.
9ab, 5a, and x are all positive terms, because the terms are preceded by addition.
-8, -10ab, -b are negative terms, because the terms are preceded by subtraction.

Constants:
A term with no variables is a constant. In the expression the only constant is -8.

COEFFICENTS:
Only terms with variables have coefficients.
The coefficient is the number located at the front of the term including the sign of the term.
If a variable term does not have a number at the front, then:
if the term is positive, the coefficient is 1
if the term is negative, the coefficient is -1

In the expression:
15 is the coefficient of 15x
9 is the coefficient of 9ab
-10 is the coefficient of -10ab
5 is the coefficient of 5a
1 is the coefficient of x
-1 is the coefficient of -b

LIKE TERMS:
Like terms are terms that have the same variables in them.

In the expression:
15x and -x are "like terms" because they both have the variable x.
9ab and -10ab are "like terms" because they both have the product of variables ab.

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