Expanding & Simplifying Algebraic Expressions

Multiplying a monomial into brackets, dividing expressions by a monomial, and substituting values to find the numerical value of an expression — the core Grade 8 algebra skills, with worked examples and a quiz.

"Expanding" means removing brackets by multiplying them out. It is the distributive property from Term 1, now with letters — and it is the skill that everything in Grade 9 algebra is built on.

1Multiplying a monomial by a binomial

Expanding as areas: 3(x + 4) is one rectangle split into two, giving 3x + 12.

a(b + c) = ab + ac

The term outside multiplies every term inside the bracket — not just the first one.

Worked ExampleExpand: 3(x + 4)

1
Multiply 3 by x: 3 × x = 3x.
First term inside.
2
Multiply 3 by 4: 3 × 4 = 12.
Second term inside — don't forget it.
3
Answer: 3x + 12.
Write the results with their signs.

Worked ExampleExpand: 2x(3x − 5)

1
2x × 3x = 6x².
Multiply numbers (2×3=6) and letters (x×x=x²) separately.
2
2x × (−5) = −10x.
Keep the negative sign.
3
Answer: 6x² − 10x.

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Very common slip: writing 3(x + 4) = 3x + 4. The 3 must reach the 4 as well, giving 3x + 12.

2Expanding then collecting like terms

Worked ExampleExpand and simplify: 2(x + 3) + 4(x − 1)

1
Expand each bracket: 2x + 6 and 4x − 4.
Handle one bracket at a time.
2
Write it all out: 2x + 6 + 4x − 4.
3
Collect like terms: (2x + 4x) + (6 − 4) = 6x + 2.
Group x-terms and constants separately.

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When a minus sits in front of a bracket, it changes every sign inside: 5 − 2(x + 3) = 5 − 2x − 6 = −2x − 1.

3Dividing by a monomial

Worked ExampleSimplify: (12x³ + 8x²) ÷ 4x

1
Divide each term separately: 12x³ ÷ 4x and 8x² ÷ 4x.
Split the division across the + sign.
2
12x³ ÷ 4x = 3x² (12÷4 = 3, x³÷x = x²).
Divide the numbers, subtract the exponents.
3
8x² ÷ 4x = 2x.
8÷4 = 2, x²÷x = x.
4
Answer: 3x² + 2x.

4Substitution — finding the value of an expression

Worked ExampleFind the value of 3x + 2y if x = 4 and y = −1

1
Replace the letters with brackets: 3( ) + 2( ).
Using brackets prevents sign errors.
2
3(4) + 2(−1) = 12 + (−2).
Substitute the given values.
3
= 10.
Adding a negative means subtracting.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
Expand: 5(x + 2)
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5x + 10
2
Expand: 4(2a − 3)
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8a − 12
3
Expand: 3x(x + 5)
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3x² + 15x
4
Expand: −2(y − 4)
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−2y + 8
5
Expand and simplify: 3(x + 2) + 2(x + 1)
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3x+6+2x+2 = 5x + 8
6
Expand and simplify: 6 − 3(x − 2)
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6 − 3x + 6 = −3x + 12
7
Simplify: (10x² + 5x) ÷ 5x
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2x + 1
8
Find the value of 4a − b if a = 3 and b = 5.
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12 − 5 = 7