Question

Simplify (3a – 2b)^2 – 2a (3a – 2b) – (3a + 2b)^2

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

=>(3a-2b)²-2a(3a-2b)-(3a+2b)²

Identity used here :

(a+b)²=a²+b²+2ab

(a-b)²=a²+b²-2ab

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

Now, expanding the terms :

=>9a²+4b²-12ab-6a²+4ab-(9a²+4b²+12ab)

Concept:-

plus minus=minus ( but sign of greater value)

minus minus =plus (but put sign of -)

=>9a²+4b²-12ab-6a²+4ab-9a²-4b²-12ab

Solving first and third term :

=>9a²-9a²+4b²-4b²-12ab-12ab-6a²+4ab

Here , 9a² and -9a² are like terms one is of positive and another of negative so,plus minus =minus and it gets cancelled mean zero.

Similarly,+4b²-4b² are both like terms one is positive and another is negative so,plus minus=minus and it gets cancelled.

=>-12ab-12ab-6a²+4ab

Here, -12ab & -12ab both are like terms both are negative so,minus minus =plus but we put sign of - .

=>-24ab-6a²+4ab

-24ab and 4ab are both like term so,plus minus =minus (but sign of bigger value )

=>-20ab-6a²

=>-6a²-20ab

Taking -2a as common

=>-2a(3a+10b)

∴ -2a(3a+10b) is the answer