b) Factorise: 16a2 – 25b2 + 60 bc – 36c2
Answers
=16a²-[(5b)²-2.5b.6c+(6c)²]
=(4a)²- (5b-6c)²
=(4a+5b-6c)(4a-5b+6c)
ANS:- (4a+5b-6c)(4a-5b+6c)
The answer to the factorisation is, (4a+5b-6c) (4a-5b+6c)
Given : The given algebraic expression is, (16a²-25b²+60bc-36c²)
To find : The factorisation of the given algebraic expression.
Solution :
We can simply solve this mathematical problem by using the following mathematical process. (our goal is to do the factorisation of the given algebraic expression)
Here, we will be using the necessary algebraic formula, to factorise the given algebraic expression.
So,
= 16a²-25b²+60bc-36c²
= 16a²- (25b²-60bc+36c²) [Taking -1 common]
= 16a² - [(5b)² - (2×5b×6c) + (6c)²]
= 16a² - (5b-6c)²
= (4a)² - (5b-6c)²
= (4a+5b-6c) (4a-5b+6c)
(This cannot be further factorised, that's why this will be considered as the final result.)
Used formula :
- a²-2ab+b² = (a-b)²
- a²-b² = (a+b) (a-b)
Hence, the answer to the factorisation is, (4a+5b-6c) (4a-5b+6c)