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What is A times A?

Level 7-8 Algebra - Linear Brackets

Expand linear brackets and simplify expressions. Use the distributive law to multiply terms, collect like terms, and solve KS3 questions with care and confidence.

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Fascinating Fact:

The distributive law makes expansion possible, it says a(b + c) = ab + ac, a key rule behind every bracket.

In KS3 Maths, you expand linear brackets using the distributive law, then simplify by collecting like terms. This skill supports solving equations, rearranging formulas, and checking algebraic work efficiently.

Key Terms

Distributive law: A rule that lets you multiply a term outside a bracket by each term inside, e.g., a(b + c) = ab + ac.
Expand: Remove brackets by multiplication, then write the result as a sum or difference of terms.
Like terms: Terms with exactly the same variables and powers (e.g., 3x and 5x) that can be combined.

Frequently Asked Questions (Click to see answers)

How do I expand a single bracket like 3(x + 4)?

Multiply the 3 by each term inside: 3 × x = 3x and 3 × 4 = 12. So 3(x + 4) = 3x + 12.

What does “collect like terms” mean in KS3 algebra?

It means combine terms with the same variable and power. For example, 2x + 5x becomes 7x, and 6 ? 4 becomes 2.

How do I expand and simplify (x + 3)(x + 2)?

Multiply each term in the first bracket by each term in the second: x(x + 2) + 3(x + 2) = x² + 5x + 6.

Try These Related Quizzes

1 .

What is a times a?

a²

a x 2

A letter multiplied by itself gives us the square of the letter

2 .

What is x³ times x⁵?

15x

x^{3 + 5}

x⁸

When multiplying powers, we add them together

3 .

What is x⁸ / x⁶?

x²

x⁴

x⁶

When dividing powers we take one from the other

4 .

How else could you represent x⁶ + x⁸?

x¹⁴

x⁶

x⁸

None of the above

If you add powers together you multiply and if you deduct powers you divide. You would need to know the value of x in order to represent it in another way after adding or subtracting

5 .

What are the four terms derived from the following linear brackets (x + 3)(x - 4)?

x² - 4x - 3x - 12

x² - 4x + 3x - 12

x² - 4x + 3x + 12

x² + 4x + 3x - 12

Two like terms (+ and + or - and -) will equal a plus; two unlike terms (+ and -) will equal a minus

6 .

What are the 4 terms derived from the following linear brackets (x - 3)(x - 4)?

x² - 4x - 3x - 12

x² - 4x - 3x + 12

x² - 4x + 3x + 12

x² + 4x - 3x + 12

Don't forget a minus times a minus equals a plus but a minus times a plus equals a minus

7 .

What are the 4 terms derived from the following linear brackets (a - 1)(a - 6)?

a² - 6a - a - 6

a² - 6a + a + 6

a² + 6a - a + 6

a² - 6a - a + 6

Remember - a minus times a minus equals a plus but a minus times a plus equals a minus

8 .

What are the 4 terms derived from the following linear brackets (x - 7)(x + 9)?

x² + 9x - 7x + 63

x² + 9x + 7x - 63

x² + 9x - 7x - 63

x² - 9x - 7x - 63

Did you remember that a minus times a minus equals a plus but a minus times a plus equals a minus?

9 .

The anwer to question 5 above was x² - 4x +3x - 12. How could this be simplified?

2x - 7x - 12

x² - x - 12

x² - 7x + 12

x² + 7x - 12

'Simplifying' an expression means 'gathering together' all the 'like units'. For instance x + 2x becomes 3x; 4a - 5a becomes -a etc.

10 .

The answer to question 8 above was x² + 9x - 7x - 63. How could this be simplified?

2x + 2x - 63

x² - 2x - 63

x² + 2x - 63

x² + 2x + 63

Because 9x - 7x = 2x

You can find more about this topic by visiting BBC Bitesize - Equations

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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