Page 91 - Maths Skills - 8

Factorisation 89

Example 5: Factorise the following:

(i) x – 9 (ii) 4m – 49 (iii) 3p – 48p
2
2
3
Solution: (i) x – 9 (ii) 4m – 49 (iii) 3p – 48p
2
2
3
= x – 3 2 = (2m) – 7 2 = 3p (p – 16)
2
2
2
= (x + 3) (x – 3) = (2m + 7) (2m – 7) = 3p (p – 4 )
2
2
= 3p (p + 4) (p – 4)
Example 6: Evaluate (using factors): 301 × 300 – 300 3
2
Solution: 301 × 300 – 300 = 300 [301 – 300 ]
2
3
2
2
= 300 [(301 + 300) (301 – 300)] [ a – b = (a + b) (a – b]
2
2
∴
= 300 × 601 × 1 = 180300
Exercise 6.2
Factorise the following algebraic expressions by using suitable identity:

1. 4x – 25 2. a x – 25 3. 1 – 36y 4. 2x – 18
2
2 2
4
2
5. 4x + 24xy + 36y 6. 4x – 1 7. m + 22m + 121 8. –2y + 12y – 18
2
2
2
2
2
16
9. am + 49a – 14am 10. x y – 64 11. –bx – 12bx – 36b 12. 16x – 100
2 2
2
2
2
13. 25a – c d 14. 5a + 10a + 5 15. t + 18t + 81 16. x + 20x + 100
2
2
2
2 2
2
17. m + 16m +64 18. 4a – b + 6b – 9 19. 121 – (x – 5) 20. (3p – 4q) – 81a 2
2
2
2
2
2
FACTORISATION BY SPLITTING THE MIDDLE TERM OF A TRINOMIAL X + BX + C
2
The polynomial (x + a) (x + b) on expanding takes the following form.
(x + a) (x + b) = x + (a + b) x + ab = x + (Sum of constant terms)x + (product of constant terms).
2
2
Thus, in order to factorise the given polynomial, we find the coefficients whose sum equals the coefficients of x
and the product equals the constant term of the polynomial.
To factorise a given polynomial, the following steps should be followed: Fact-o-meter
1. Write the trinomial in the standard form The algebraic expression
i.e. ax + bx + c (descending order of powers of literal) of the form ax + bx + c
2
2
2. Suppose, trinomial is ax bx c is called as quadratic
2
containing +ve sign trinomial.
Then find the product of a and c. Now find the factors of this product in such a way so that the sum of
these factors will be equal to b.
3. Suppose, trinomial is ax bx c
2
containing –ve sign
Then find the product of a and c. Now find the factors of this product in such a way so that the
difference of these factors will be equal to b.
Let us learn through examples.