Think of grouping. Notice that first two terms have a common factor 2y;
Step 1 Check it
Step 2
6xy - 4y = 2y (3x - 2)
What about the last two terms? Observe them. If you change their orde
- 9x + 6, the factor ( 3x - 2) will come out;
-9x + 6 = -3 (3x) + 3 (2)
= -3 (3x - 2)
Step 3 Putting (a) and (b) together,
6xy - 4y + 6 - 9x = 6xy - 4y - 9x + 6
= 2y (3x - 2) - 3 (3x - 2)
= (3x - 2) (2y - 3)
The factors of (6xy - 4y +6-9 x) are (3x - 2) and (2y - 3).
EXERCISE 14.1
1. Find the common factors of the given terms.
(1) 12x, 36 (ii) 2y, 22xy (ii) 14 pq, 28p?q?
(iv) 2x, 3x2, 4 (v) 6 abc, 24ab?, 12 a b
(vi) 16 x), - 4x2, 32x
(vii) 10 pq, 20qr, 30rp
(viii) 3x y3, 10x y2,6 x y z
minn the following expressions.
Answers
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Factors of natural numbers
You will remember what you learnt about factors in Class VI. Let us take a natural number, say 30, and write it as a product of other natural numbers, say
30 = 2 × 15
= 3 × 10 = 5 × 6
Thus, 1, 2, 3, 5, 6, 10, 15 and 30 are the factors of 30. Of these, 2, 3 and 5 are the prime factors of 30 (Why?)
A number written as a product of prime factors is said to be in the prime factor form; for example, 30 written as 2 × 3 × 5 is in the prime factor form.
The prime factor form of 70 is 2 × 5 × 7.
The prime factor form of 90 is 2 × 3 × 3 × 5, and so on.
Similarly, we can express algebraic expressions as products of their factors. This is what we shall learn to do in this chapter.