Expanding & Simplifying Single Brackets (Cambridge International IGCSE Mathematics)

Expanding One Bracket

How do I expand a bracket?

• The expression 3x (x + 2) means 3x multiplied by the bracket (x + 2)

  • 3*x *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
  • 3*x *(x + 2) expands to $3x\times x+3x\times2$ which simplifies to $3x^{2}+6x$

• Beware of minus signs

  • Remember the rules − × − = + − × + = −
  • It helps to put brackets around negative terms

Worked Example (a) Expand 4x (2x−3).

Answer:

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

4x×2x+4x×(−3)

Simplify

$8x^{2}-12x$

(b) Expand −7x (4−5y).

Answer:

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

(−7x)×4+(−7x)×(−5y)

Simplify and remember that multiplying two negatives gives a positive

$-28x+35xy$

Expand & Simplify

How do I simplify brackets that are added together?

• First expand both brackets separately

  • 4 (x+7)+5x (3−x)

    • The first set of brackets expands to $4\times x+4\times7$ which simplifies to $4x+28$
    • The second set of brackets expands to 5x×3+5x×(−x) which simplifies to $15x-5x^{2}$
    • So 4 (x+7)+5x (3−x)=4x+28+15x−5x²

• Then collect like terms

  • $4x+15x=19x$

    • The other two terms are not like terms

  • So 4 (x+7)+5x (3−x)=19x+28−5x²

Worked Example (a) Expand and simplify 2 (x+5)+3x (x−8).

Answer:

Expand each set of brackets separately

You can keep negative terms inside brackets

2×x+2×5+3x×x+3x×(−8)

Simplify each term

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

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

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

(b) Expand and simplify 3x (x+2)−7 (x−6).

Answer:

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

• *3x×x+3x×2+(−7)×x+(−7)×(−6)

Simplify each term Remember that multiplying two negatives gives a positive

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

Collect like terms

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