Expanding Brackets and Simplifying Worksheet | Cazoom Maths Worksheets - Free Printable

Let's solve each expression step by step, following the instructions: expand the brackets and then simplify.

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🔷 Section A

We will expand each bracket using the distributive property:
> $ a(b + c) = ab + ac $

Then combine like terms.

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1) $ 7(y + 4) + 8 $
= $ 7y + 28 + 8 $
= $ 7y + 36 $

✔ Answer: $ 7y + 36 $

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2) $ 5(b + 2) + 4 $
= $ 5b + 10 + 4 $
= $ 5b + 14 $

✔ Answer: $ 5b + 14 $

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3) $ 3(a + 5) + 2a $
= $ 3a + 15 + 2a $
= $ 5a + 15 $

✔ Answer: $ 5a + 15 $

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4) $ 2(x + 6) + 7x $
= $ 2x + 12 + 7x $
= $ 9x + 12 $

✔ Answer: $ 9x + 12 $

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5) $ 4(9 + f) + 18f $
= $ 36 + 4f + 18f $
= $ 36 + 22f $

✔ Answer: $ 22f + 36 $

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6) $ 8(1 + 2g) + 5g $
= $ 8 + 16g + 5g $
= $ 8 + 21g $

✔ Answer: $ 21g + 8 $

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7) $ 9 + 3(c + 4) $
= $ 9 + 3c + 12 $
= $ 3c + 21 $

✔ Answer: $ 3c + 21 $

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8) $ 11 + 5(6d + 5) $
= $ 11 + 30d + 25 $
= $ 30d + 36 $

✔ Answer: $ 30d + 36 $

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9) $ 7x + 4(2x + 12) $
= $ 7x + 8x + 48 $
= $ 15x + 48 $

✔ Answer: $ 15x + 48 $

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10) $ 12a + 9(5 + 2a) $
= $ 12a + 45 + 18a $
= $ 30a + 45 $

✔ Answer: $ 30a + 45 $

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🔷 Section B

Now we include more complex expressions, including negative signs and subtraction of brackets.

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1) $ 6(3d - 1) + 8 $
= $ 18d - 6 + 8 $
= $ 18d + 2 $

✔ Answer: $ 18d + 2 $

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2) $ 5(6x - 2) + 2 $
= $ 30x - 10 + 2 $
= $ 30x - 8 $

✔ Answer: $ 30x - 8 $

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3) $ 7 - 3(8f + 6) $
= $ 7 - (24f + 18) $
= $ 7 - 24f - 18 $
= $ -24f - 11 $

✔ Answer: $ -24f - 11 $

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4) $ -9 - (4j + 5) $
= $ -9 - 4j - 5 $
= $ -4j - 14 $

✔ Answer: $ -4j - 14 $

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5) $ 8 - (1 - k) $
= $ 8 - 1 + k $
= $ 7 + k $

✔ Answer: $ k + 7 $

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6) $ -2h - 4(6h - 1) $
= $ -2h - 24h + 4 $
= $ -26h + 4 $

✔ Answer: $ -26h + 4 $

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7) $ 5b(2b - 3) + 8 $
= $ 10b^2 - 15b + 8 $

✔ Answer: $ 10b^2 - 15b + 8 $

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8) $ 7c(2c - 5) - 3 $
= $ 14c^2 - 35c - 3 $

✔ Answer: $ 14c^2 - 35c - 3 $

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9) $ 9 - 2e(3 - 5e) $
First expand: $ 2e(3 - 5e) = 6e - 10e^2 $
So:
$ 9 - (6e - 10e^2) = 9 - 6e + 10e^2 $
= $ 10e^2 - 6e + 9 $

✔ Answer: $ 10e^2 - 6e + 9 $

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10) $ xy - x(y - 1) $
First expand: $ x(y - 1) = xy - x $
So:
$ xy - (xy - x) = xy - xy + x = x $

✔ Answer: $ x $

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✔ Final Answers Summary

#### Section A
1. $ 7y + 36 $
2. $ 5b + 14 $
3. $ 5a + 15 $
4. $ 9x + 12 $
5. $ 22f + 36 $
6. $ 21g + 8 $
7. $ 3c + 21 $
8. $ 30d + 36 $
9. $ 15x + 48 $
10. $ 30a + 45 $

#### Section B
1. $ 18d + 2 $
2. $ 30x - 8 $
3. $ -24f - 11 $
4. $ -4j - 14 $
5. $ k + 7 $
6. $ -26h + 4 $
7. $ 10b^2 - 15b + 8 $
8. $ 14c^2 - 35c - 3 $
9. $ 10e^2 - 6e + 9 $
10. $ x $

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📝 Key Tips:

- Always multiply each term inside the bracket by the number outside.
- Be careful with negative signs: e.g., $ -(a + b) = -a - b $
- Combine like terms (same variables and powers).
- For algebraic multiplication like $ 5b(2b - 3) $, multiply $ 5b \times 2b = 10b^2 $, etc.

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