Expanding Single Brackets (Edexcel GCSE Maths: Foundation)

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Maths

Expanding One Bracket

How do I expand a bracket?

The expression 3x (x + 2) means 3x multiplied by the bracket (x + 2)
- 3x is the term outside the bracket
  - this is sometimes called a factor
- and x + 2 are the terms inside the bracket
Expanding the brackets means multiplying the outside term by each term on the inside
- This will remove (get rid of) the brackets
- 3x (x + 2) expands to $3 x \times x + 3 x \times 2$ which simplifies to $3 x^{2} + 6 x$
Beware of minus signs
- Remember the rules
  − × − = +
  − × + = −
- It helps to put brackets around negative terms

Worked example

(a)

Expand

4 x (2 x - 3)

Multiply the $4 x$ term outside the brackets by both terms inside the brackets

$4 x \times 2 x + 4 x \times (- 3)$

Simplify

$8 x^{2} - 12 x$

(b)

Expand

- 7 x (4 - 5 y)

Multiply the $- 7 x$ outside the brackets by both terms inside the brackets

$(- 7 x) \times 4 + (- 7 x) \times (- 5 y)$

Simplify and remember that multiplying two negatives gives a positive

$- 28 x + 35 x y$

Expand & Simplify

How do I simplify brackets that are added together?

First expand both brackets separately
- $4 (x + 7) + 5 x (3 - x)$
  - The first set of brackets expands to $4 \times x + 4 \times 7$ which simplifies to $4 x + 28$
  - The second set of brackets expands to $5 x \times 3 + 5 x \times (- x)$ which simplifies to $15 x - 5 x^{2}$
  - So $4 (x + 7) + 5 x (3 - x) = 4 x + 28 + 15 x - 5 x^{2}$
Then collect like terms
- - The other two terms are not like terms
- So $4 (x + 7) + 5 x (3 - x) = 19 x + 28 - 5 x^{2}$

Worked example

(a)

Expand and simplify

2 (x + 5) + 3 x (x - 8)

Expand each set of brackets separately

You can keep negative terms inside brackets

$2 \times x + 2 \times 5 + 3 x \times x + 3 x \times (- 8)$

Simplify each term

$2 x + 10 + 3 x^{2} - 24 x$

Collect like terms (the 2x and the -24x)

$- 22 x + 10 + 3 x^{2}$

(b)

Expand and simplify

3 x (x + 2) - 7 (x - 6)

Expand each set of brackets separately
Be careful: the second set of brackets has a -7 in front, not +7

$3 x \times x + 3 x \times 2 + (- 7) \times x + (- 7) \times (- 6)$

Simplify each term
Remember that multiplying two negatives gives a positive

$3 x^{2} + 6 x - 7 x + 42$

Collect like terms

$3 x^{2} - x + 42$

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