Factors

You learnt how to find the H.C.F. (Highest Common Factor) of algebraic terms or expressions by expressing them in product form and finding the common factors.
Factorisation is the reverse process of multiplication. It means breaking an algebraic expression into product of two or more factors.
You learnt factorisation of algebraic expressions by the method of common factors, difference of squares and grouping. You also learnt factorisation of trinomials.

Exercise

Factorise the following (1 - 17):

x² + 5x + 6
x² - 8x + 7
x² + 6x - 7
y² + 7y - 18
y² - 7y - 18
a² - 3a - 54
2x² - 7x + 6
6x² + 13x - 5
6x² + 11x - 10
6x² - 7x - 3
x² - 2x + 1
4x² - 12x + 9
5 - 4x - 12x²
x (12x + 7) - 10
2x² + 13xy - 24y²
2a²b² - 7ab - 30
(a - b)² + 6 (a - b) + 8
Work out the value of
(i) (100002)² - (99998)²
(ii)
(iii) (1001)²
(iv) (999)²

Answers

1. (x + 2)(x + 3)             2. (x - 1)(x - 7)
3. (x + 7)(x - 1)              4. (y + 9)(y - 2)
5. (y - 9)(y + 2)              6. (a + 6)(a - 9)
7. (x - 2)(2x - 3)            8. (3x - 1)(2x + 5)
9. (2x + 5)(3x - 2)         10. (3x + 1)(2x - 3)
11. (x - 1)²                    12. (2x - 3)²
13. (1 - 2x)(5 + 6x)        14. (4x + 5)(3x - 2)
15. (x + 8y)(2x - 3y)      16. (ab -6)(2ab + 5)
17. (a - b + 4)(a - b + 2)
18.(i) 800000    (ii) 24 (iii) 1002001      (iv) 998001