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🍬honors algebra ii review

key term - Like Terms

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Definition

Like terms are terms in an algebraic expression that have the same variable raised to the same power. This similarity allows like terms to be combined through addition or subtraction, making it easier to simplify expressions and perform algebraic operations. Identifying like terms is essential for effective factoring and manipulating algebraic expressions, as it helps to organize and streamline calculations.

5 Must Know Facts For Your Next Test

  1. Only the coefficients of like terms can be combined while keeping the variable part unchanged.
  2. For example, in the expression $$3x + 5x$$, both terms are like terms because they share the same variable, $$x$$, allowing them to be combined to make $$8x$$.
  3. Terms with different variables or powers are not like terms; for example, $$3x$$ and $$4y$$ cannot be combined.
  4. Like terms can significantly simplify expressions during factoring by reducing the number of terms to work with.
  5. When factoring an expression, recognizing and combining like terms can reveal common factors, making it easier to rewrite the expression in a more manageable form.

Review Questions

  • How can you identify like terms in an expression, and why is this important for simplifying algebraic expressions?
    • To identify like terms in an expression, look for terms that have identical variable parts and exponents. This is important for simplifying expressions because combining like terms reduces complexity and helps to create a clearer equation. For example, recognizing that $$2x^2$$ and $$3x^2$$ are like terms allows you to combine them into $$5x^2$$, simplifying calculations in further operations.
  • Given the expression $$4a^2 + 3b + 6a^2 - 2b$$, how would you combine the like terms?
    • In the expression $$4a^2 + 3b + 6a^2 - 2b$$, the like terms are $$4a^2$$ and $$6a^2$$ as well as $$3b$$ and $$-2b$$. Combining these gives you $$10a^2 + b$$. This process illustrates how identifying and combining like terms streamlines the expression into a more usable form.
  • Evaluate the importance of recognizing like terms when factoring polynomials. How does this skill affect the overall process?
    • Recognizing like terms when factoring polynomials is crucial because it allows you to group and simplify components of the polynomial efficiently. For instance, understanding that you can combine terms before attempting to factor reveals common factors more easily. This skill directly impacts the overall process by reducing errors, speeding up calculations, and leading to a clearer path for finding factored forms or solutions to equations.