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AQA GCSE · Question 11 · Algebra
Here are three terms.
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xy, x², 5y²
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Alec multiplies two of these terms.
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Work out the three possible fully simplified answers.
Here are three terms.
<br>
xy, x², 5y²
<br>
Alec multiplies two of these terms.
<br>
Work out the three possible fully simplified answers.
How to approach this question
1. Identify the three possible pairs of terms you can multiply.
2. For each pair, multiply the coefficients (the numbers) first.
3. Then, for each variable (x and y), multiply them together by adding their powers. Remember that x is x¹ and y is y¹.
4. Write down the three simplified results.
Full Answer
There are three possible pairs of terms to multiply:
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**1. (xy) × (x²)**
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= x × y × x²
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= (x × x²) × y
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= x¹⁺² × y
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= x³y
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**2. (xy) × (5y²)**
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= x × y × 5 × y²
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= 5 × x × (y × y²)
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= 5 × x × y¹⁺²
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= 5xy³
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**3. (x²) × (5y²)**
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= 5x²y²
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**Answers: x³y, 5xy³, 5x²y²**
We need to find the product of each possible pair of the three terms: xy, x², and 5y².
**Pair 1: (xy) and (x²)**
Product = (xy) * (x²)
Group the x terms together: (x * x²) * y
Using the law of indices (xᵃ * xᵇ = xᵃ⁺ᵇ), we get x¹ * x² = x¹⁺² = x³.
So, the product is x³y.
**Pair 2: (xy) and (5y²)**
Product = (xy) * (5y²)
Multiply the coefficients: 1 * 5 = 5.
Group the y terms together: x * (y * y²)
Using the law of indices, y¹ * y² = y¹⁺² = y³.
So, the product is 5xy³.
**Pair 3: (x²) and (5y²)**
Product = (x²) * (5y²)
Multiply the coefficients: 1 * 5 = 5.
The variables are different, so we just write them next to each other.
So, the product is 5x²y².
The three possible answers are x³y, 5xy³, and 5x²y².
Common mistakes
✗ Incorrectly applying the laws of indices, for example multiplying the powers instead of adding them (e.g., writing x * x² = x²).
✗ Forgetting to multiply the numerical coefficients.
✗ Finding only one or two of the possible products.
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