Question

Factorise : a-b-a^2+b^2

Answer 1

$(a - b) - ( {a}^{2} - {b}^{2} ) \\ = (a - b) - (a - b)(a + b)$
$= (a - b)(1 - a - b)$

Answer 2

Answer:

a - b -a² + b² = (a-b)(1-a-b)

Step-by-step explanation:

To find,

The factors of a - b -a² + b²

Recall the formula

a² - b² = (a+b)(a-b)

Solution

a - b -a² + b² =  a - b -(a² - b²)

=( a - b )- [(a+b)(a-b)}(since a² - b² = (a+b)(a-b))

(a-b) is common in both the terms,

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

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

∴ a - b -a² + b² = (a-b)(1-a-b)

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