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Senior Phase Mathematics: Grade 7 – 9 Learner book
Unit 2.2: Calculating algebraic expressions
Multiplication:
To multiply, you don't need like terms. Any terms can be multiplied together.
STEPS: Worked example: 3x2z × x2y3 × (–4xy3)
1. Multiply the coefficients (with their signs). 3 × 1 × –4 = –12
2. Multiply the variables with the same x2 × x2 × x = x5 and y3 × y3 = y6
–12 x4z y6
base by adding the exponents.
3. If there are powers that don't have the –12 x4 y6 z
same bases, write them in your final
answer leaving out the ൈ sign.
4. If your final answer has more than one
variable, list them in alphabetical order.
Worked examples: Simplify the following expressions Grade 8 & 9
1. 2݉ ൈ െ3݉ଶ
ൌ െ6݉ଷ
2. ‫ݔ‬ଷ‫ݕ‬ସ ൈ ‫ݖݕݔ‬ଶ
ൌ ‫ݔ‬ସ‫ݕ‬ହ‫ݖ‬ଶ
The distributive property:
Multiplication is distributed over addition and subtraction. You may have used this property
before to multiply numbers: Remember BEDMAS.
8 ൈ 36 ൌ 8ሺ30 ൅ 6ሻ ൌ 8 ൈ 30 ൅ 8 ൈ 6 ൌ 240 ൅ 42 ൌ 282 Multiply before adding.
Worked examples: Simplify the following:
1. 3ሺ2‫ ݔ‬൅ 1ሻ ൌ 6‫ ݔ‬൅ 3 Be careful with the
2. െ3ܽሺܽଶ ൅ 4ܽ െ 2ሻ ൌ െ3ܽଷ െ 12ܽଶ ൅ 6ܽ
+ signs and the – signs
Product of two binomials: F: first terms
O: outer terms
Multiply both terms in the first bracket by both terms in the second I: inner terms
bracket. L: last terms
Worked examples: Grade 9
Simplify the following 2. ሺ2ܽ െ ܾሻሺ4ܽ െ 3ܾሻ
FL ൌ 8ܽଶ െ 6ܾܽ െ 4ܾܽ ൅ 3ܾଶ
ൌ 8ܽଶ െ 10ܾܽ ൅ 3ܾଶ
1. ሺ‫ ݔ‬൅ 3ሻሺ2‫ ݔ‬െ 1ሻ First multiply, then look
I for like terms to add. In
O this example, െ‫ ݔ‬and ൅6‫ݔ‬
ൌ 2‫ݔ‬ଶ െ ‫ ݔ‬൅ 6‫ ݔ‬െ 3 are like terms which
ൌ 2‫ݔ‬ଶ ൅ 5‫ ݔ‬െ 3 simplify to ൅5‫ݔ‬.
Winning Teams & Olico 36
