In this section we look at how to simplify expressions, in particular, how to remove brackets from both formulae and equations.

*Collecting like terms*

Examples

*a* + *a* + *a* = 3*a*

*a* + *b* + *a* = 2*a* + *b*

2y + 8y = 10y

x + x^2 + x^2 = x + 2x^2

Only like terms can be collected

Simplify the following expressions,

(a) | 4a + 2b + 3a + 6b = | 7a + 8b |
---|---|---|

(b) | 3x - 4y + 2x - y = | 5x - 5y |

(c) | x^2 + 4x + 2x^2 - x = | 3x^2 + 3x |

(d) | 4a^2 + a + 2a^2 - 3a = | 6a^2 - 2a |

*Expanding Brackets*

Every term in each bracket must be multiplied by every other item.

x(4x + 2) | = x × 4x + x × 2 |

= 4x^2 + 2x |

(x + 1)(x + 4) | = x × x + x × 4 + 1 × x + 1 × 4 |

= x^2 + 4x + x + 4 | |

= x^2 + 5x + 4 |

Alternatively, you can expand brackets using the 'box' method, as shown opposite.

(x + 1)(x + 4) = x^2 + 1x + 4x + 4 = x^2 + 5x + 4

Expand each of the following:

(a) | 2(x + 3) | 2(x + 3) = 2 × x + 2 × 3 = 2x + 6 |
---|---|---|

(b) | 4(2x - 6) | 4(2x - 6) = 4 × 2x - 4 × 6 = 8x - 24 |

(c) | x(x + 2) | x(x + 2) = x × x + x × 2 =x^2 + 2x |

(d) | 2x(3x - 2) | 2x(3x - 2) = 2x × 3x - 2x × 2 = 6x^2 - 4x |

Expand,

(a)

(x + 6)(x + 3)

(x + 6)(x + 3) | = x × x + x × 3 + 6 × x + 6 × 3 |

= x^2 + 3x + 6x + 18 | |

= x^2 + 9x + 18 |

or alternatively, using the box method,

(x + 6)(x + 3) | = x^2 + 6x + 3x + 18 |

= x^2 + 9x + 18 |

(b)

(x + 4)(2x - 5)

(x + 4)(2x - 5) | = x × 2x - x × 5 + 4 × 2x - 4 × 5 |

= 2x^2 - 5x + 8x - 20 | |

= 2x^2 + 3x - 20 |

Again, using the box method,

(x + 4)(2x - 5) | = 2x^2 + 8x - 5x - 20 |

= 2x^2 + 3x - 20 |

Note: To type indeces on this page use ^ sign. e.g. *n*^{2}: