How do I identify coefficients, constant terms, and like terms of the expression?
bozo
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.
To identify coefficients, constant terms, and like terms of an expression, follow these steps:
1. Coefficients: Look for the numerical factors that are multiplied by the variables. Coefficients are the numbers that appear before the variables. For example, in the expression 3x + 4y - 2z, the coefficients are 3, 4, and -2.
2. Constant terms: Constant terms are the numbers without any variables attached to them. They are terms that do not involve variables. In the expression 3x + 4y - 2z + 7, the constant term is 7.
3. Like terms: Like terms are the terms that have the same variable raised to the same power. For example, in the expression 5x + 2y + 3x - 4y, the like terms are 5x and 3x (both have x as the variable) and 2y and -4y (both have y as the variable).
4. Simplify the expression by combining like terms: Combine the coefficients of the like terms and keep the variables unchanged. In the example above, combining the like terms gives 8x - 2y.
By following these steps, you can easily identify the coefficients, constant terms, and like terms in an expression.
To identify coefficients, constant terms, and like terms in an expression, you need to understand the definitions of each term.
1. Coefficients: Coefficients are the numerical values multiplied by variables in an expression. They indicate the relative size or scale of the variable. To identify coefficients, look for the numbers that are directly multiplied by variables in the expression. For example, in the expression 3x + 2y - 5z, the coefficients are 3, 2, and -5.
2. Constant Terms: Constant terms are the numbers or values that do not have any variables attached to them. They are standalone values in an expression and do not change. To identify constant terms, look for numbers without variables or letters attached to them. For example, in the expression 3x + 2y - 5z + 7, the constant term is 7.
3. Like Terms: Like terms are terms that have the same variables raised to the same power. To identify like terms, look for terms that have the same variables with the same exponents. For example, in the expression 3x + 2y - 5z + 7 - 2x + 4y + 3z, the like terms are 3x and -2x (both have x), 2y and 4y (both have y), and -5z and 3z (both have z).
Knowing these definitions, you can analyze the expression to identify coefficients, constant terms, and like terms correctly.