How do I expand brackets by multiplication?

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It's worth remembering FOIL: First, Outside, Inside, Last.

Say we have the following:

(a+b)(c+d), where a,b,c and d are positive integers.

Using FOIL, we have:

 (First) + (Outside) + (Inside) + (Last)

   ac     +       ad        +    bc       +    bd

Examples:

Expand the following brackets:

1. (2x+3)(4x+6) = (F) 8x(O) 12x + (I) 12x + (L) 18

                          = 8x+ 24x + 18

2. (6x-1)(2x2+4) = (6x)(2x2) + 4(6x) + (-1)(2x2) + (-1)(4)

                          = 12x+ 24x - 2x- 4

3. (x-1)(2x+4)(3x-6)  (Note: For this example, first expand the first two brackets, then expand the result with the third bracket, as follows):

= (2x2+2x-4)(3x-6)    (To expand this, multiply the first term in the 1st bracket by the 1st term and 2nd term in the 2nd, the 2nd term in the 1st by the 1st and 2nd term in the 2nd bracket, the 3rd term in the 1st bracket by the 1st and 2nd terms in the 2nd bracket, as follows):

= 6x- 12x+ 6x- 12x - 12x + 24

= 6x- 6x- 24x + 24

                          

                                

Liam D. GCSE Maths tutor, A Level Maths tutor

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