Algebra: Combining Like Terms

Combining Like Terms

• Combining like terms is a fundamental algebraic skill.

• Like terms are terms that contain the same variables raised to the same powers.

• Coefficients of like terms can be added or subtracted to simplify expressions.

• For example, '3x' and '5x' are like terms because both have the variable 'x' raised to the power of 1.

• Similarly, '7y²' and '2y²' are like terms because both have the variable 'y' raised to the power of 2.

• The terms '2x' and '2y' are not like terms because they have different variables.

• '4x²' and '4x' are not like terms because the variables are raised to different powers.

• These types of terms can be combined by adding or subtracting the coefficients.

• Constants are also like terms and can be combined. For example, '3' and '7' can be combined to equal '10'.

• To combine like terms, add or subtract the coefficients and keep the same variable and exponent.

• Example:

  • Simplify the expression:  3x + 5x + 2

  • The terms '3x' and '5x' are like terms. Adding the coefficients (3 + 5 = 8) gives us '8x'.

  • The term '2' is a constant and does not have a like term so it stays the same.

  • Putting the result together, you have '8x+2'.

• Example:

  • Simplify the expression:  7y² + 2y² - 4y

  • Combine the like terms (7y² and 2y²). (7 + 2 = 9)

  • This gives us '9y²'.

  • The term '-4y' doesn't have a like term to combine with, so it stays as it is, giving the result '9y² - 4y'.

• Important Note:  Only like terms can be combined; combining unlike terms will not simplify the entire expression. For example, You cannot combine 'x' and 'y' directly.

• When an expression has terms with negative coefficients, apply the rules for adding and subtracting integers.

• Example:

  • Simplify the expression: 4x - 3y + 2 + 4x - 8y -1

  • Combine the like terms (+4x and +4x giving 8x). (-3y and -8y giving -11y). (+2 and -1 giving +1 or just 1.)

  • This gives us to result '8x - 11y + 1'

• Combining Like Terms is a useful skill for solving equations, simplifying algebraic expressions, and for a wealth of other processes.

Test your understanding of combining like terms in algebra. This essential skill involves identifying and simplifying terms with the same variables and exponents. Dive into examples and practice to cement your knowledge.