5 Algebraic Expressions
By studying this lesson, you will be able to;
² find the value of simple algebraic expressions by substituting directed
numbers,
² expand the product of two binomial expressions of the form (x ± a) (x ± b),
² verify the expansion of the product of two binomial expressions by considering
areas.
Algebraic expressions
Do the following exercise to review what you have learnt in grade 8, related to
algebraic expressions.
Review Exercise
1. Expand the following expressions.
a. 5 (x + 2) b. 3 (y + 1) c. 4 (2m + 3)
d. 3 (x – 1) e. 4 (3 – y) f. 2 (3x – 2y)
g. – 2 (y + 3) h. – 3 (2 + x) i. – 5 (2a + 3b)
j. – 4 (m – 2) k. – (5 – y) l. – 10 (–3b – 2c)
2. Expand the following expressions.
a. x (a + 2) b. y (2b – 3) c. a (2x + 3y)
d. 2a (x + 5) e. 2b(y – 2) f. 3p (2x – y)
g. (–3q) (p + 8) h. (–2x) (3 – 2y) i. (– 5m) (x – 2y)
3. Find the value of each of the following expressions when x = 3 and y = – 2.
a. x + y b. x – y c. 3x – 2y
d. – 2x + y e. 2(x + y) f. 3 (2x– y)
4. Expand and simplify each of the following expressions.
a. 3 (x + y) + 2 (x – y) b. 5(a + b) + 4 (a + c)
c. 4 (a + b) + 3 (2a – b) d. 2(a – b) + (2a – b)
e. 5 (m + n) + 2 (m + n) f. 3(m + n) – (m – n)
g. 5 (x – y) – 3 (2x + y) h. 2(3p – q) – 3 (p – q)
i. – 4 (m + n) + 2 (m + 2) j. – 4 (a – b) – 2 (a – b)
60
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, 5.1 Substitution
In grade 8, you learnt to find the value of an algebraic expression by substituting
integers for the unknown terms. Let us now find out how to obtain the value of an
algebraic expression by substituting directed numbers.
♦ 20 adults and 16 children went on a trip. Each adult was given x amount of bread
and each child was given y amount of bread for breakfast.
Let us write the total amount of bread that was distributed as an algebraic expression.
Amount of bread given to the 20 adults = 20x
Amount of bread given to the 16 children = 16y
Total amount of bread that was distributed = 20x + 16y
Let us find out the total amount of bread that was distributed, if an adult was given
half a loaf of bread and a child was given a quarter loaf of bread.
1 1
Then x = 2 and y = 4 . To find out the total amount of bread that was
1 1
distributed, x = 2 and y = 4 should be substituted in the expression
20x + 16y '
Accordingly, the total number of loaves of bread that were = 20 × 1 + 16 × 1
distributed 2 4
= 10 + 4
= 14
Example 1
1
Find the value of each of the following algebraic expressions when a = 2 .
i. 2a + 3 ii. 6 – 4a iii. 3a – 1
1 1 1
2a + 3 = 2 × 2 + 3
3a – 1 = 3 × 2 – 1 6 – 4a = 6 – 4 × 2
3
=1+3 = 2 –1 =6–2
=4 =4 3–2
=
2
1
= 2
61
For free distribution
By studying this lesson, you will be able to;
² find the value of simple algebraic expressions by substituting directed
numbers,
² expand the product of two binomial expressions of the form (x ± a) (x ± b),
² verify the expansion of the product of two binomial expressions by considering
areas.
Algebraic expressions
Do the following exercise to review what you have learnt in grade 8, related to
algebraic expressions.
Review Exercise
1. Expand the following expressions.
a. 5 (x + 2) b. 3 (y + 1) c. 4 (2m + 3)
d. 3 (x – 1) e. 4 (3 – y) f. 2 (3x – 2y)
g. – 2 (y + 3) h. – 3 (2 + x) i. – 5 (2a + 3b)
j. – 4 (m – 2) k. – (5 – y) l. – 10 (–3b – 2c)
2. Expand the following expressions.
a. x (a + 2) b. y (2b – 3) c. a (2x + 3y)
d. 2a (x + 5) e. 2b(y – 2) f. 3p (2x – y)
g. (–3q) (p + 8) h. (–2x) (3 – 2y) i. (– 5m) (x – 2y)
3. Find the value of each of the following expressions when x = 3 and y = – 2.
a. x + y b. x – y c. 3x – 2y
d. – 2x + y e. 2(x + y) f. 3 (2x– y)
4. Expand and simplify each of the following expressions.
a. 3 (x + y) + 2 (x – y) b. 5(a + b) + 4 (a + c)
c. 4 (a + b) + 3 (2a – b) d. 2(a – b) + (2a – b)
e. 5 (m + n) + 2 (m + n) f. 3(m + n) – (m – n)
g. 5 (x – y) – 3 (2x + y) h. 2(3p – q) – 3 (p – q)
i. – 4 (m + n) + 2 (m + 2) j. – 4 (a – b) – 2 (a – b)
60
For free distribution
, 5.1 Substitution
In grade 8, you learnt to find the value of an algebraic expression by substituting
integers for the unknown terms. Let us now find out how to obtain the value of an
algebraic expression by substituting directed numbers.
♦ 20 adults and 16 children went on a trip. Each adult was given x amount of bread
and each child was given y amount of bread for breakfast.
Let us write the total amount of bread that was distributed as an algebraic expression.
Amount of bread given to the 20 adults = 20x
Amount of bread given to the 16 children = 16y
Total amount of bread that was distributed = 20x + 16y
Let us find out the total amount of bread that was distributed, if an adult was given
half a loaf of bread and a child was given a quarter loaf of bread.
1 1
Then x = 2 and y = 4 . To find out the total amount of bread that was
1 1
distributed, x = 2 and y = 4 should be substituted in the expression
20x + 16y '
Accordingly, the total number of loaves of bread that were = 20 × 1 + 16 × 1
distributed 2 4
= 10 + 4
= 14
Example 1
1
Find the value of each of the following algebraic expressions when a = 2 .
i. 2a + 3 ii. 6 – 4a iii. 3a – 1
1 1 1
2a + 3 = 2 × 2 + 3
3a – 1 = 3 × 2 – 1 6 – 4a = 6 – 4 × 2
3
=1+3 = 2 –1 =6–2
=4 =4 3–2
=
2
1
= 2
61
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