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Study Guide : Factorising Quadratics And Expanding Double Brackets

Learner Guide

 

Maths


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Factorising Quadratics and Expanding double brackets

L . O to be able to expand and factorise two brackets to form

a quadratic equation in the form x2 + bx + c.


Expanding

Expanding as we have seen before involves removal of the product brackets.

Here the same principle applies however you can’t just multiply the constant

on the outside of the brackets by each one on the inside otherwise you will

have an incomplete expansion.

 

There are two main methods: The GRID method and the FOIL method.

 

The Grid method

This method involves separating the terms inside the brackets and multiplying

each one individually.

 

Example 1:

Expand ( x + 2 ) ( x + 5 )

    X        X   +2
    X       X2   +2X
   +5    +5X    +10

 

Step 1:

Multiply each adjacent parts of the grid together. Notice how the grid use +2 and not just

2.x X x = x2+2 X x = +2x+5 X x = +5x

+2 X +5 = +10

Step 2:

Add all the terms together x2+2x+5x +10

 Step 3:

Simplify any like terms

x2 + 7x + 10

 

Example 2:

Expand ( x – 9 ) ( x – 8 )

XX-9
XX2-9X
-8-8X+72

 

Step 1:

Multiply each adjacent parts of the grid together. Notice how the grid use +2 and not just 2.x X x = x2

-9 X x = -9x

-8 X x = -8x

-9 X -8 = +72 (Remember – x – = +)

Step 2:

Add all the terms together x2-9x-8x+72

 

Step 3:

Simplify any like terms

x2 – 17x + 72


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Related Topics


Expressions-and-formulae                                         Index-notation

Solving-linear-equations                                            Expanding-and-factorising

 

 



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