Question

can we write a^n+b^n=(a+b)^n​

Answer 1

Answer:

a^n + b^n is not equal to ( a + b )^n

Step-by-step explanation:

To prove a^n + b^n is not equal to ( a + b )^n

let a = 2 , b = 3 and n = 2

Suppose that the given condition is true

therefore ,

(2)²+ (3)² = (2+3)²

4 + 9 = (2)² + (3)² + 2(2*3)

13 = 4 + 9 + 12

13 = 25

hence 13 is not equal to 25

Therefore our supposition is false , hence proved

Answer 2

Answer:

No, we can't.

This is because,

if you take an example where, a=2 ,b=3 and n=5

So,

${a}^{n} = {2}^{5} = 32$

${b}^{n} = {3}^{5} = 243$

$32 + 243 = 275$

$then \: {a}^{n} + {b}^{n} = 275$

$a + b = 2 + 3 = 5$

${(a + b)}^{n} = {(2 + 3)}^{5} = {5}^{5} = 3125$

$since \: 275 \: is \: not \: equal \: to \: 3125$

$so \: we \: cannot \: say \: {a}^{n } + {b}^{n} = {(a + b)}^{n}$

Hope it helps you!

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