# Math Expressions Worksheet With Answers - Grade 7 And 8 - University Of Waterloo - 2013 Page 3

We can use this idea to also evaluate (a + b)
(c + d):
(a + b)
(c + d) = a
(c + d) + b
(c + d)
= a
c + a
d + b
c + b
d
= ac + ad + bc + bd
As you can see, every term in the ﬁrst sum is multiplied by every term in the second sum.
To remember this, the mnemonic FOIL is used. FOIL is an acronym:
Firsts
Multiply the ﬁrst term in each sum (a and c).
Outsides Multiply the two terms on the outsides (a and d).
Insides
Multiply the innermost terms (b and c).
Lasts
Multiply the last term in each sum (b and d).
FOIL can also be represented visually in a chart:
a
b
c
ac
bc
d
Reminder: When working with the Distributive Property, it is important to remember how
to multiply and divide negative and positive numbers.
• a positive multiplied or divided by a positive will result in a positive number
• a negative multiplied or divided by a negative will result in a positive number
• a positive multiplied or divided by a negative will result in a negative number
Example
2
5
(2 + 5)
(6
3) = (2)(6) + (2)( 3) + (5)(6) + (5)( 3)
6
12
30
= 12
6 + 30
15
3
6
15
= 21
12 + 30
6
15 = 21
We can check that this is right by using our BEDMAS rules:
(2 + 5)
(6
3) = 7
3
= 21
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