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5
5
1. The sum of 3x a and –4x a is ............... .
3
2. The product of (4p qr)(–7qr) = ............... .
1 −1
3
2
3. Find the value of 5x – 4x + for x = .
8 2
4. Find the product of (6a – 7a – 3) and (2a – 3).
2
Factorisation of Natural Numbers

Let us consider the number 70. If we try to write 70 as a product of two or more numbers, then
we get

70 = 1 × 70 = 2 × 5 × 7
= 2 × 35 = 5 × 14 = 5 × 2 × 7
= 7 × 10 = 7 × 2 × 5

Thus, 1, 2, 5, 7, 10, 14, 35, and 70 are the factors of 70. Also, we observe that 2 × 5 × 7 is the product
of prime factors in every case given above.
Therefore, the form of factorisation where all factors are
prime numbers is called the prime factorisation. Quick Check
Thus, prime factorisation of 70 = 2 × 5 × 7. Express the given numbers as
product of primes:
Similarly, we can express an algebraic expression as the 1. 48 2. 96
product of its irreducible factors.

Factorisation of Algebraic Expressions

When an algebraic expression is factorised, it is written as the product of its factors and these
factors can be numbers, variables or algebraic expressions.

For example,
• 5x can be written as 5 × x, where 5 and x are factors of 5x. Remember

• 7xy can be written as 7 × x × y, where 7, x and y are irreducible factors ‘1’ is the factor of every term,
of 7xy. In algebraic expressions, the word ‘irreducible’ is used in but unless required, ‘1’ need
the place of ‘prime’. not be shown separately.
5a(b + 3) can be written as 5 × a × (b + 3), where 5, a and (b + 3)
are irreducible factors of 5a(b + 3). 7 × (xy) is not the irreducible

Thus, the process of finding two or more expressions/irreducible Note: form of 7xy. Since the factor
factors whose product is the given expression is known as xy can be further expressed
factorisation. as x × y.
The expressions that are multiplied to obtain the given algebraic expression are called the factors
of the given algebraic expression.
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For example, (x + 2) and (x – 2) are the factors of x – 4, since (x + 2)(x – 2) = x – 4.
Factorisation

Algebraic Expression Factors Note: Factorisation is the reverse process
of multiplication.
Multiplication

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