Question

Factorize:
(i) 9x² - y2 + 4y – 4

Answer 1

ANSWER:

   Factorisation of the above expression is (3x+y-2)(3x-y+2).

GIVEN:

   9x²-y²+4y-4

TO FIND:

   Factorise the above expression.

SOLUTION:

= 9x²-y²+4y-4

= 9x²-(y²-4y+4)

= 9x²-[(y)²-2(2)(y) +(2)²]

= (3x)² -(y-2)²

= (3x+y-2)(3x-y+2)

Factorisation of the above expression is (3x+y-2)(3x-y+2).

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab