Expanding & Simplifying Single Brackets

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 $3x\times x+3x\times 2$ which simplifies to $3x^2+6x$

Beware of minus signs

• Remember the rules
  −  ×  −  =  +
  −  ×  +  =  − 

• It helps to put brackets around negative terms

First expand both brackets separately

• $4\left(x+7\right)+5x\left(3-x\right)$ 

  • The first set of brackets expands to $4\times x+4\times 7$ which simplifies to $4x+28$

  • The second set of brackets expands to $5x\times 3+5x\times \left(-x\right)$ which simplifies to $15x-5x^2$

  • So $4\left(x+7\right)+5x\left(3-x\right)=4x+28+15x-5x^2$

Then collect like terms

• $4x+15x=19x$

  • The other two terms are not like terms

• So $4\left(x+7\right)+5x\left(3-x\right)=19x+28-5x^2$