Question

Factorize (a+3b).(2a +b) – (2a+b).(a+b) + (3a+2b)^2​

please answer asap!

Answer 1

Ànswer

Step by step explanation

$\sf(a + 3b)(2a + b) - (2a + b)(a + b) + {(3a + 2b)}^{2}$

Now , expanding the terms :

=>a(2a+b)+3b(2a+b)-[2a(a+b)+b(a+b)]+(3a+2b)²

Identity used here :

✰(a+b)²=a²+b²+2ab

=>2a²+ab+3ab+3b²-[2a²+2ab+ab+b²]+(3a)²+(2b)²+2(3a)(2b)

=>Now ,removing the brackets and expanding the terms :

=>2a²+ab+3ab+3b²-2a²-2ab-ab-b²+9a²+4b²+12ab

=>Rearranging the terms and make like terms together:

=>2a²-2a²+ab-ab+3ab-2ab+3b²-b²+9a²+4b²+12ab

2a² will be cancelled as plus minus = minus.Similarly, ab will be cancelled.

=>3ab-2ab+3b²-b²+9a²+4b²+12ab

=>ab+2b²+9a²+4b²+12ab

=>9a²+2b²+4b²+ab+12ab

=>9a²+6b²+13ab

Further solve : we can take 3 as common as 9 and 6 are multiples of 3

=>3(3a²+2b²)+13ab