Question

factorise a²-4b+2a-b²-3

Answer 1

${a}^{2} - 4b + 2a - {b}^{2} - 3 \\ {a}^{2} + 2a + 1 - {b}^{2} - 4b - 3 - 1 \\ add \: \: + 1 \: \: and \: - 1 \: in \: the \: equation \: and \: rearrange \\ = {a}^{2} + 2a + 1 -( {b}^{2} + 4b + 4) \\ = ( {a + 1)}^{2} - ( {b + 2)}^{2}$now use the identity {a}^2-{b}^2= (a+b)(a-b)
=(a+1+b+2)(a+1-b-2)
=(a+b+3)(a-b-1)

Answer 2

a² + 2a + 1 — [ b² + 4b + 4 ]

using identity

(a—b)² = a² + b² - 2ab
&
(a+b)² = a²+b²+2ab

now

=> (a + 1)² — (b + 2)²

using identity

a² - b² = (a+b) (a-b)

=> (a+1+b+2) (a+1-b-2)

=> (a + b + 3) ( a - b -1)

is the factor.


———————————————————

Hope it will help you..✌✌