Study guide: Evaluate and Rewrite Algebraic Expressions
Use whole-number exponents, substitute values, distribute, and combine equivalent terms.
Ideas to explain in your own words
- A whole-number exponent tells how many equal factors are multiplied.
- A variable is a symbol representing a number.
- The distributive property multiplies each term in a sum by the outside factor.
- Like terms contain the same variable part.
Useful vocabulary
- coefficient
- A numerical factor multiplying a variable.
- equivalent expressions
- Expressions giving the same value for every allowed variable input.
Watch your reasoning
- Base times exponent is not exponentiation.
- A coefficient outside x² is not automatically part of the squared base.
- Matching one chosen input alone does not prove two arbitrary expressions equivalent.
- Constants and variable terms are not like units.
A worked review example
For 4³, write 4×4×4=64. Multiplying 4×3 gives twelve, which is not the same operation. In 2×3²+1, calculate 3²=9 first, then 2×9+1=19. The exponent attaches only to its base three. Write out the repeated factors before calculating. Base times exponent is not exponentiation. Mark the base and exponent, then draw one factor box for each exponent count.
Make a practice plan
- Read an Exponent as Repeated Multiplication: Evaluate 5² and 2⁴. Expected: 25 and 16.
- Substitute a Value While Preserving Expression Structure: Evaluate 4(y+2) for y=3. Expected: 20.
- Distribute to Rewrite an Equivalent Expression: Factor 8x+24. Expected: 8(x+3).
- Combine Like Terms and Recognize Their Units: Simplify 6a+2+4a+7. Expected: 10a+9.