KS3. Algebra. 2. Expanding Brackets - Maths with David - Free Printable

Sure! Let's solve Question 5 and Question 6 step by step, expanding and simplifying each expression.

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## ✔ Question 5: Expand and simplify

We use the distributive property:
a(b + c) = ab + ac, then combine like terms.

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(a) 5(y + 3) + 2(y + 7)

Expand:
= 5y + 15 + 2y + 14

Combine like terms:
= (5y + 2y) + (15 + 14)
= 7y + 29

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(b) 6(2w + 5) + 9(w + 2)

Expand:
= 12w + 30 + 9w + 18

Combine:
= (12w + 9w) + (30 + 18)
= 21w + 48

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(c) 3(y - 2) + 4(2y + 5)

Expand:
= 3y - 6 + 8y + 20

Combine:
= (3y + 8y) + (-6 + 20)
= 11y + 14

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(d) 7(2g + 3) - 5(g + 2)

Expand:
= 14g + 21 - 5g - 10

Combine:
= (14g - 5g) + (21 - 10)
= 9g + 11

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(e) 6(x - 2) - 4(x - 8)

Expand:
= 6x - 12 - 4x + 32 ← Note: minus times minus is plus!

Combine:
= (6x - 4x) + (-12 + 32)
= 2x + 20

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(f) 2(3y - 8) - 5(2y - 1)

Expand:
= 6y - 16 - 10y + 5 ← minus 5 times -1 is +5

Combine:
= (6y - 10y) + (-16 + 5)
= -4y - 11

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(g) 8(5 + 2m) + 3(5 - 3m)

Expand:
= 40 + 16m + 15 - 9m

Combine:
= (16m - 9m) + (40 + 15)
= 7m + 55

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(h) 4(w + 7) - 2(2w + 1)

Expand:
= 4w + 28 - 4w - 2

Combine:
= (4w - 4w) + (28 - 2)
= 0w + 26 = 26

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(i) 9(1 + 2y) + 3(3 - y)

Expand:
= 9 + 18y + 9 - 3y

Combine:
= (18y - 3y) + (9 + 9)
= 15y + 18

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## ✔ Question 6: Expand and simplify

Here we have expressions where a variable multiplies a binomial — still use distributive property, then combine like terms.

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(a) w(w + 5) + w(w + 7)

Expand each:
= w² + 5w + w² + 7w

Combine:
= (w² + w²) + (5w + 7w)
= 2w² + 12w

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(b) 2g(4g + 3) + g(g - 7)

Expand:
= 8g² + 6g + g² - 7g

Combine:
= (8g² + g²) + (6g - 7g)
= 9g² - g

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(c) n(n - 4) - n(5 - n)

Expand:
= n² - 4n - [5n - n²] ← Distribute the minus sign!
= n² - 4n - 5n + n²

Combine:
= (n² + n²) + (-4n - 5n)
= 2n² - 9n

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(d) 2e(4e + 3) - 3e(e - 5)

Expand:
= 8e² + 6e - [3e² - 15e]
= 8e² + 6e - 3e² + 15e

Combine:
= (8e² - 3e²) + (6e + 15e)
= 5e² + 21e

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(e) a(3 + c) + c(a + 2)

Expand:
= 3a + ac + ac + 2c

Combine like terms (ac + ac = 2ac):
= 3a + 2ac + 2c

*(Note: 3a and 2c are not like terms with ac, so we leave as is.)*

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(f) m(a + 7) - a(4 - 3m)

Expand:
= am + 7m - [4a - 3am]
= am + 7m - 4a + 3am

Combine like terms (am + 3am = 4am):
= 4am + 7m - 4a

*(Order doesn't matter — you can write as 4am - 4a + 7m if preferred.)*

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(g) 8c(8 - 3a) + 3(4 - c)

Expand:
= 64c - 24ac + 12 - 3c

Combine like terms (64c - 3c = 61c):
= -24ac + 61c + 12

*(We usually write terms with variables first, constants last.)*

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(h) 5y(3y + z) - 2y(4y - 3z)

Expand:
= 15y² + 5yz - [8y² - 6yz]
= 15y² + 5yz - 8y² + 6yz

Combine:
= (15y² - 8y²) + (5yz + 6yz)
= 7y² + 11yz

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(i) 4c(3c - c²) - 2c²(4 - 5c)

Expand each part:

First: 4c(3c - c²) = 12c² - 4c³
Second: -2c²(4 - 5c) = -8c² + 10c³

Now combine:
= (12c² - 8c²) + (-4c³ + 10c³)
= 4c² + 6c³

*(Usually written in descending powers: 6c³ + 4c²)*

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## ✔ Final Answers:

Question 5:

(a) 7y + 29
(b) 21w + 48
(c) 11y + 14
(d) 9g + 11
(e) 2x + 20
(f) -4y - 11
(g) 7m + 55
(h) 26
(i) 15y + 18

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Question 6:

(a) 2w² + 12w
(b) 9g² - g
(c) 2n² - 9n
(d) 5e² + 21e
(e) 3a + 2ac + 2c
(f) 4am + 7m - 4a
(g) -24ac + 61c + 12
(h) 7y² + 11yz
(i) 6c³ + 4c²

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Let me know if you’d like to see any step explained further! 😊