Quadratic Expressions Worksheets Page 3
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36number and algebra
7.2 Expanding algebraic expressions
Binomial expansion
• Consider the rectangle of length a + b and width c + d shown below. Its area is equal to
(a + b) (c + d).
a
b
The diagram shows that 1 a + b 2 1 c + d 2 = ac + ad + bc + bd.
c
ac
bc
d
ad
bd
factorised form
expanded form
• Expansion of the binomial expression (x + 3) (x + 2) can be shown by this area model.
3
x
3 × x
x × x = x
2
x
= 3x
1 x + 3 2 1 x + 2 2 = x
3 × 2
2 × x = 2x
2
= 6
Expressed mathematically this is:
+ 2x + 3x + 6
2
= x
+ 5x + 6
2
factorised form
expanded form
• There are several methods that can be used to expand binomial factors.
FOIL method
FOIL
• The word
provides us with an acronym for the expansion of a binomial
product.
F
• First: multiply the first terms in each bracket
(x + a)(x − b)
O
• Outer: multiply the two outer terms
(x + a)(x − b)
I
• Inner: multiply the two inner terms
(x + a)(x − b)
L
• Last: multiply the last terms in each bracket
(x + a)(x − b)
Maths Quest 10 + 10A
270
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