Multiply algebraic terms
Objective. Use multiplication notation and index conventions.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Multiplying algebraic terms means multiplying the numerical coefficients together and combining the variable parts using index rules. When multiplying the same variable, add the powers, so x²×x³=x⁵. For example, 3a×4a becomes 3×4×a×a=12a². When different variables are multiplied, such as 2x×3y, they simply sit next to each other as 6xy since they cannot combine further. Always multiply coefficients first, then handle each variable separately using index notation.
Worked example
Simplify the product of the algebraic terms 5x²y and 3xy³.
- 1Multiply the coefficients: 5×3=15.
- 2Combine the x terms: x²×x=x³.
- 3Combine the y terms: y×y³=y⁴.
- 4Write the simplified term together.
Answer: 15x³y⁴
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Practice
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Start practisingCommon mistake. Pupils often multiply the powers instead of adding them, turning x²×x³ into x⁶ rather than x⁵. Remind them that multiplying terms with the same base means adding the indices.
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