EXPANDING EXPRESSIONS
(3 brackets)
(a+b)(c+d)(e+f) = (a.c + a. d + b. c + b. d)(e+f)
. f. + a .d .e + a.d.f + b. c. e + b. c. f + b. d. e + b. d. f
= a c. e. + a c
Removing brackets from
expressions by multiplying
out the factors within the
brackets
for instance (2x-3)(x-2)(x+3)
You must expand the brackets by multiplying the
expressions in the corrrect order shown above
Once you have expanded out the expressions
you must simplify
Expand the first two brackets and simplify before
expanding the last bracket
Simple questions will require you to just
expand and simplify expressions
3 2
+ + x+ x x
Three brackets will give a quadratic in the form
Higher level questions will require you to
expand and simplify expressions before
using more complex skills
Make sure you take into account the + and - signs
infront of the factors as:
+x+ = + (3x4 = 12)
+x- = - (3x-4 = -12)
-x- = + (-3x-4 = 12)
Expanding expressions is the opposite process to factorising
practice Question
Expand
Simplify
(2x-3)(x-2)
Step One
Step Two
Expand first two brackets by multiplying out
factors and then simplify
Exapand last bracket by
multiplying out factors
and then simplify
(2x-3)(x-2)(x+3)
(2x2- 7x + 6)(x+3)
2x x. + 2x .-2 + -3. x + -3. -2
2x 2x. - 7x .x + 6.x + 2x2. 3 - 7x. 3
+ 6. 3
2x 2+ -4x + -3x + 6
2x 3- 7x 2+ 6x + 6x2 - 21x + 18
2x - 4x - 3x + 6
2
Collect like
terms
2x 2- 4x - 3x + 6
-4x
+
-3x = -7x
2x - 7x + 6
2
studytime.co.nz
facebook.com/studytimenewzealand
Rearrange
and collect like
terms
Simplify like
2x 3- 7x 2+ 6x2 - 21x + 6x + 18
-21x + 6x = -15x
-7x + 6x2 = -x
2
And get 2x - x - 15x +18
3
2