Question

factories by expressing into a perfect square-a^2-4a+3+2b-b^2

Answer 1

Hi ,

a² - 4a + 3 + 2b - b²

= a² - 4a + 4 - 1 + 2b - b²

= ( a² - 4a + 4 ) - ( 1 - 2b + b² )

= (a² - 2 × a × 2 + 2² ) - ( 1²-2×1×b+b²)

= ( a - 2 )² - ( 1 - b )²

= ( a - 2 + 1 - b ) [ ( a - 2 ) - ( 1 - b ) ]

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

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

I hope this helps you.

: )

Answer 2

Hey friend, Harish here.

Here is your answer:

To factorize: 

a² - 4a + 3 + 2b - b²

Solution:

⇒ [tex]a\² - 4a + 3 + 2b - b^{2} = a^{2} - 4a + 4 - 1 + 2b - b^{2} [/tex]

(Here we have added and subtracted one).↑

⇒ $(a^{2} - 4a + 4) - (1 - 2b + b^{2})$

⇒ $(a-2)^{2} - (1-b)^{2}$

We know that, a² - b² = (a+b)(a-b)

⇒ $[(a-2)+(1-b)] \times [(a-2)-(1-b)]$

⇒ $(a-b-1)(a+b-3)$
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Hope my answer is helpful to you.