By now you'll have done a good deal of work in KS3 Maths all about algebra. You'll be familiar with equations, variables, powers and many other aspects of the subject. But how well do you understand linear brackets?

Equations can often be simplified by removing any brackets. You may have to 'get-rid' of two sets of adjoining brackets so that you can work out the values of the terms within the brackets. Each term in the first bracket needs to be multiplied by each term in the second bracket.

Be careful if there are any powers in your equations. If there are then remember this piece of advice: when multiplying powers, we add them together so y^{2} x y^{4} = y^{6}. When dividing powers we take one from the other so y^{9} ÷ y^{5} = y^{4}.

The best way to beat the brackets is to practise. Try this quiz and see how well you can deal with them. Take your time and consider your answers carefully. Good luck!

1.

What is a times a?

a^{2}

a2

2a

a x 2

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

2.

What is *x*^{3} times *x*^{5}?

15*x*

8*x*

When multiplying powers, we add them together

3.

What is *x*^{8} / *x*^{6}?

2*x*

When dividing powers we take one from the other

4.

How else could you represent x^{6} + x^{8}?

x^{14}

x^{6}

x^{8}

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)?

x^{2} - 4x - 3x - 12

x^{2} - 4x + 3x - 12

x^{2} - 4x + 3x + 12

x^{2} + 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)?

x^{2} - 4x - 3x - 12

x^{2} - 4x - 3x + 12

x^{2} - 4x + 3x + 12

x^{2} + 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)?

a^{2} - 6a - a - 6

a^{2} - 6a + a + 6

a^{2} + 6a - a + 6

a^{2} - 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)?

x^{2} + 9x - 7x + 63

x^{2} + 9x + 7x - 63

x^{2} + 9x - 7x - 63

x^{2} - 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 x^{2} - 4x +3x - 12. How could this be simplified?

2x - 7x - 12

x^{2} - x - 12

x^{2} - 7x + 12

x^{2} + 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 x^{2} + 9x - 7x - 63. How could this be simplified?

2x + 2x - 63

x^{2} - 2x - 63

x^{2} + 2x - 63

x^{2} + 2x + 63

Because 9x - 7x = 2x

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