Question

Factorise 36a^2 + 4b^2 + 5c^2 − 24ab − 4√5bc + 12√5ca by using suitable identity. step by step answer will be marked brainliest

Answer 1

Hey Pretty Stranger!

$\sf \: 36 {a}^{2} + {4b}^{2} + 5 {c}^{2} - 24ab - 4 \sqrt{5} bc + 12 \sqrt{5} ca$

We are gonna factorise it now, pay attention *clears throat*

$\sf \: ( {6a})^{2} + ({ - 2b})^{2} + ({ \sqrt{5}c })^{2} + 2(6a)( - 2b) + 2( - 2b)( \sqrt{5} + 2( \sqrt{5}c)(6a)$

We have got the form of :

$\sf \: {a}^{2} + {b}^{2} + {c}^{2} + 2ab \: + 2bc + 2ca$

and we know that it stands for (a+b+c)², remember? (if not, then go learn identities ;-;)

Here,

• a = 6a

• b = -2b and

• c = √5c

So,

$\sf \: [6a + ( - 2b) + \sqrt{5} c]^{2}$

$\sf \: (6a - 2b + \sqrt{5} c)(6a - 2b + \sqrt{5} c)$

yayy, we did it ._.