Questions
(1) Factorise x + x^2Y^2 - 1/(xy) - y
(2) Factorise completely 4x^2 - y^2 + 4y - 4
(3) Without using a calculator (Hint : use factorisation),
find the value of (88888)^2 - 88895 x 88881
Answer
(1) x + x^2Y^2 - 1/(xy) - y
= x(1 + xy^2) - 1/(xy)[1 + xy^2]
= (1+ xy^2)[x- 1/(xy)]
Alternative Answer
x^2(1/x+y^2) - 1/y(1/x+y^2)
= (x^2-1/y)(1/x+y^2)
(2) 4x^2 - y^2 + 4y - 4
= (2x)^2 - (y-2)^2
= (2x+y-2)(2x- (y-2))
= (2x+y-2)(2x-y+2)
(3) (88888)^2 - 88895 x 88881
= (88888)^2 - (88888+7)(88888 - 7)
= (88888)^2 - [(88888)^2 - 7^2]
= (88888)^2 - (88888)^2 + 7^2
= 49