Math Problem Statement

I can recognise like terms and simplify expressions using like terms.

Solution

I can see that the image contains exercises related to recognizing and simplifying like terms.

Top Section:

Task: Recognize like terms

  1. The exercise asks to tick pairs of like terms.

    • Like terms are those that have the same variables raised to the same power, even if their coefficients are different.

    The circled pairs are:

    • 5x5x and 3x-3x: These are like terms because both involve xx.
    • 2a2a and aa: These are like terms because both involve aa (note: aa is equivalent to 1a1a).
    • 4ab4ab and 3ba3ba: These are like terms because ab=baab = ba (commutative property).

The uncircled pairs are not like terms because either their variables are different or their exponents do not match.

Bottom Section:

Task: Simplify expressions using like terms

  1. Simplifying involves combining the like terms.

    The given answers are:

    • 4c2d5c+6d=9c8d4c - 2d - 5c + 6d = 9c - 8d: This correctly combines like terms for cc and dd.
    • 2x24x+35x2+4x2=7x2+8x12x^2 - 4x + 3 - 5x^2 + 4x - 2 = 7x^2 + 8x - 1: This correctly combines like terms for x2x^2, xx, and the constant terms.

Would you like further details or explanations on any part of this solution? Here are 5 related questions to think about:

  1. How do we define like terms more formally?
  2. Why are abab and baba considered like terms even though their order differs?
  3. What happens if we try to combine terms that aren't like terms?
  4. Can two constants (like 55 and 77) be considered like terms?
  5. How can we apply this process to equations instead of expressions?

Tip: Always focus on the variables and their exponents to identify like terms, as coefficients can vary.

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Math Problem Analysis

Mathematical Concepts

Algebra
Like Terms
Simplification of Expressions

Formulas

Combining like terms: ax + bx = (a+b)x
Combining constants or coefficients with the same variables

Theorems

Commutative Property of Multiplication
Basic Algebraic Simplification

Suitable Grade Level

Grade 6-8