Algebra worksheet for expanding single brackets with 10 problems.

You’ve uploaded an image with a math worksheet titled “Expanding Single Brackets”, dated 13th Apr. The task is to expand each of the 10 expressions (a–j) by distributing the number outside the bracket to each term inside.

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🔢 What does “expanding single brackets” mean?

It means using the distributive property:

> a(b + c) = ab + ac

We multiply the term outside the bracket by each term inside the bracket, and then simplify if needed.

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Let’s solve each one step-by-step:

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✔ a) `4(x + 3)`

Multiply 4 by both terms inside:
= `4 × x + 4 × 3`
= 4x + 12

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✔ b) `3(x + 4)`

= `3 × x + 3 × 4`
= 3x + 12

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✔ c) `4(x - 5)`

= `4 × x - 4 × 5`
= 4x - 20

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✔ d) `-2(x - 1)`

Be careful with the negative sign!
= `-2 × x + (-2) × (-1)` ← because minus times minus = plus
= -2x + 2

*(Note: Some students write this as -2x + 2, which is correct.)*

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✔ e) `2(x + 2)`

= `2 × x + 2 × 2`
= 2x + 4

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✔ f) `-5(2 - a)`

Distribute -5 to both terms:
= `-5 × 2 + (-5) × (-a)` ← minus times minus = plus
= -10 + 5a

*(You can also write it as 5a - 10 — both are correct.)*

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✔ g) `4(1 - c)`

= `4 × 1 - 4 × c`
= 4 - 4c

*(Or -4c + 4 — same thing.)*

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✔ h) `-5(4 + b)`

= `-5 × 4 + (-5) × b`
= -20 - 5b

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✔ i) `4(5 + x)`

= `4 × 5 + 4 × x`
= 20 + 4x or 4x + 20

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✔ j) `6(1 + k)`

= `6 × 1 + 6 × k`
= 6 + 6k or 6k + 6

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## 📝 Final Answers:

| Problem | Answer |
|---------|---------------|
| a | 4x + 12 |
| b | 3x + 12 |
| c | 4x - 20 |
| d | -2x + 2 |
| e | 2x + 4 |
| f | -10 + 5a |
| g | 4 - 4c |
| h | -20 - 5b |
| i | 20 + 4x |
| j | 6 + 6k |

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💡 Tip: Always check the signs carefully — especially when there's a negative number outside the bracket. A negative times a positive is negative; a negative times a negative is positive.

Let me know if you’d like to practice more or see how to factor back from these expanded forms! 😊