Question

Factorise a2 – b2 – (a + b) 2

Answer 1

Question should be:

• Factorise a²-b²-(a+b)²

ANSWER:

• Factorisation of above expression is (-2b)(a+b).

GIVEN:

• a²-b²-(a+b)²

TO FIND:

• Factorise the above expression.

SOLUTION:

= a²-b²-(a+b)²

= [(a)²-(b)²] -(a+b)²

= (a+b)(a-b) -(a+b)²

Taking (a+b) as common.

= (a+b)[(a-b)-(a+b)]

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

= (a+b)(-2b)

= (-2b)(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