1.

Expand each of the following using suitable identitiesplease answer this question

Answer»

Hello dear,

(4a + 2b - 3c)² we can expand by using the identity =>
(a+b+c)² = a² + b² + c² + 2(AB + BC + ca)

So,
(4a + 2b - 3c)² = (4a)² + (2b)² + (-3c)² + 2 [ 4a*2b + 2b*(-3c) + (-3c)*4a ]
= 16a² + 4b² + 9c² + 2 [ 8AB - 6bc - 12ca]
= 16a² + 4b² + 9c² + 16ab - 12bc - 24ca

Now,
(5+a)² we can expand by using the identity
=> (a+b)² = a² + b² + 2ab
So,
(5+a)² =(5)² + (a)² + 2*5*a
= 25 + a² + 10a

Now,
(2a - 3b + 5)² we can expand by using the identity
=> (a+b+c)² = a² + b² + c² + 2(ab + bc + ca)

So,
(2a - 3b + 5)² = (2a)² + (-3b)² + (5)² + 2 [ 2a*(-3b) + (-3b)*5 + 5*2a ]
= 4a² + 9b² + 25 + 2 [ (-6AB) + (-15b) + 10a ]
= 4a² + 9b² + 25 - 12ab - 30b + 20a

Hope it helps.






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