Question

Factorize:
25a2 - 962 + 12bc - 4c2

Answer 1

The factors are:- (5a-3b+2c)(5a+3b-2c)

       

       25$a^{2}$-9b²+12bc+4c²

• Here the equation in the bracket is a perfect square.

        25a²-(9b²-12bc+4c²)

        25a²-((3b)²-2×3×2bc+(2c)²)

• Hence, can be written as (3b-2c)²

• Let, (3b-2c)²=Y²

• The above equation can be written as:

        25a²-Y²

• This can be FACTORIZED by using the formula:- a²-b²=(a-b)(a+b)

        (5a-Y)(5a+Y)

• By putting the value of Y

We get

(5a-3b+2c)(5a+3b-2c)