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KS3 Mathematics

A1 Algebraic expressions

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A1.3 Multiplying terms

Contents

A1 Algebraic expressions

A1.1 Writing expressions

A1.2 Collecting like terms

A1.4 Dividing terms

A1.5 Factorising expressions

A1.6 Substitution

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Multiplying terms together

In algebra we usually leave out the multiplication sign ×.

Any numbers must be written at the front and all letters should be written in alphabetical order.

For example,

4 × a = 4a

1 × b = b We don’t need to write a 1 in front of the letter.

b × 5 = 5b We don’t write b5.

3 × d × c = 3cd

6 × e × e = 6e2

We write letters in alphabetical order.

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Using index notation

Simplify:

x + x + x + x + x = 5x

Simplify:

x × x × x × x × x = x5

x to the power of 5

This is called index notation.

Similarly,

x × x = x2

x × x × x = x3

x × x × x × x = x4

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We can use index notation to simplify expressions.

For example,

3p × 2p = 3 × p × 2 × p = 6p2

q2 × q3 = q × q × q × q × q = q5

3r × r2 = 3 × r × r × r = 3r3

2t × 2t = (2t)2 or 4t2

Using index notation

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Look at this algebraic expression:

4(a + b)

What do do think it means?

Remember, in algebra we do not write the multiplication sign, ×.

This expression actually means:

4 × (a + b)or

(a + b) + (a + b) + (a + b) + (a + b)

= a + b + a + b + a + b + a + b

= 4a + 4b

Brackets

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Expanding brackets then simplifying

Sometimes we need to multiply out brackets and then simplify.

For example, 3x + 2(5 – x)

We need to multiply the bracket by 2 and collect together like terms.

3x + 10 – 2x

= 3x – 2x + 10

= x + 10

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Expanding brackets then simplifying

Simplify

4 – (5n – 3)

We need to multiply the bracket by –1 and collect together like terms.

4 – 5n + 3

= 4 + 3 – 5n

= 7 – 5n

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Expanding brackets then simplifying

Simplify

2(3n – 4) + 3(3n + 5)

We need to multiply out both brackets and collect together like terms.

6n – 8 + 9n + 15

= 6n + 9n – 8 + 15

= 15n + 7

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Simplify

5(3a + 2b) – 2(2a + 5b)

We need to multiply out both brackets and collect together like terms.

15a + 10b – 4a –10b

= 15a – 4a + 10b – 10b

= 11a

Expanding brackets then simplifying

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Algebraic multiplication square

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Pelmanism: Equivalent expressions