Question

factorise: 1+2ab-(a²+b²)​

Answer 1

ANSWER:

• Factorisation of the above expression is (1+a-b)(1-a+b).

GIVEN:

• P(x) = 1+2ab-(a²+b²)

TO FIND:

• Factorisation of the above expression .

SOLUTION:

= 1+2ab-(a²+b²)

= 1+2ab-a²-b²

= 1-(a²+b²-2ab)

= (1)²-(a-b)²

= (1+a-b)(1-a+b)

Factorisation of the above expression is (1+a-b)(1-a+b).

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