Algebraic Expressions Involving basic Arithmetic Operations

Mathematics
with

Teacher Rifa

Algebraic Expressions Involving
Basic Arithmetic Operations

In this topic, you will be
able to :

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→ Add and subtract two
or more algebraic
expressions
→ Make generalisation
for repeated
multiplication algebraic
expressions
→ Multiply and divide
algebraic expressions
with one term

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Addition and
Subtraction of

Algebraic
Expressions

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1.We can add or subtract two

or more algebraic
expressions by grouping the
like terms

2.The sum of pair of positive
and negative numbers with
the same figure is zero

1 + (- 1) = 0

2 + (-2) = 0

Just like numbers, for
algebraic terms:

x + (-x) = 0

y + (-y) = 0

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Other examples of zero pairing,

x + x = 2x xx

(-x) + (-x) = - 2x -x -x
2x + (-2x) = 0

yyy y + y + y = 3y

-y -y -y (-y) + (-y) + (-y) = -3y
3y + ( -3y) = 0

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3. Some other examples of zero
pairing are:
a) (-2x) + 2x = -2x + 2x = 0
b) (-3y) + 3y = -3y + 3y = 0

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Add two or more
algebraic

expressions

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Example 1

Simplify (3a + 5b) + (4a - 7b)

Solution

(3a + 4b) + (4a - 7b)
= 3a + 5b + 4a - 7b
= 3a + 4a + 5b - 7b
= 7a - 2b

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Example 2

Find the sum of -3k + 4h - 3
and k + 6h - 5

Solution

(-3k + 4h - 3) - (k + 6h - 5)
= -3k + 4h - 3 + k +
6h - 5
= -3k + k + 4h + 6h -
3-5
= 2k + 10h - 8

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Subtract two or
more algebraic

expressions

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Example 1

Simplify (5p - 3) - (- 2p + 7)

Solution

(5p - 3) - (- 2p + 7)
= 5p - 3 + 2p - 7
= 5p + 2p - 3 - 7
= 7p - 10

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Example 2

Simplify (2x - 3y + 5) - (-8x -
5y + 1) + (x - 3)

Solution

(2x - 3y + 5) - (-8x - 5y
+ 1) + (x - 3)

= 2x - 3y + 5 + + 8x +
5y - 1 + x - 3
= 2x + 8x + x - 3y + 5y
+5-1-3
= 11x + 2y + 1

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Repeated
multiplication of

algebraic
expressions
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1. You have already learnt about the
square and cube of a number in
Chaper 3 . For example,

Square of 4: 42 = 4 x 4
Cube of 4: 43 = 4 x 4 x 4

The concept of power can also be
applied to variables. That is,

a x a = a2 and a x a x a = a3

2. Square and cube are the
repeated multiplication twice and
thrice respectively. If the process of
repeated multiplication is
continued, the power of the higher
degree will be produced.

a x a x a x a = a4
a x a x a x a x a = a5

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3. Repeated multiplication can also
be used in algebraic expressions

Example 1

Write each of the following in power
form.

a) (3h - 1) (3h - 1)
b) (6p + 7) (6p + 7) (6p + 7) (6p + 7)

Solution

a) (3h - 1) (3h - 1)
= (3h - 1)2

b) (6p + 7) (6p + 7) (6p + 7) (6p + 7)
= (6p + 7)4

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Thank you
and good

luck
everyone !! :]

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