How To Multiply Out Brackets

To multiply out brackets, multiply each thing in the first set of brackets by each thing in the second set. Then, you need to ‘collect like terms’. This means adding together all the plain numbers, all the ‘x’ terms, all the ‘x2‘ terms, etc.

Here’s an example. I’m using ‘.’ to mean multiply to avoid getting confused with ‘x’!
(2x + 3)(x + 4)
2x.x + 2x.4 + 3.x + 3.4
2x2 + 8x + 3x + 12
2x2 + 11x + 12

That was an easy one because there were no negatives. Be very careful with negatives and remember that negative times negative gives positive. Like this:
(3x - 3)(4x - 5)
3x.4x - 3x.5 - 3.4x + 3.5
12x2 - 15x - 12x + 15
12x2 - 27x + 15

In the National 5 exam, they often have a question where you have to multiply a bracket containing two terms with a bracket containing three terms. If you’ve been taught ‘FOIL’, it does not work here. You have to multiply each term in the first bracket by each term in the second bracket. Like this:
(x + 3)(2x2 + 5x + 6)
x.2x2 + x.5x + x.6 + 3.2x2 + 3.5x + 3.6
2x3 + 5x2 + 6x + 6x2 + 15x + 18
2x3 + 11x2 + 21x + 18

Take your time and check carefully. Especially when there are negatives:
(2x - 4)(3x2 - 2x + 5)
2x.3x2 - 2x.2x + 2x.5 - 4.3x2 + 4.2x - 4.5
6x3 - 4x2 + 10x - 122 + 8x - 20
6x3 - 16x2 + 18x - 20

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