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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