Question

give the formula for(a^5-b^5)​

Answer 1

The formula for a⁵-b⁵ is (a - b)(a⁴ + a³b² + a²b² + ab³ + b⁴).

Given:

a⁵-b⁵

To Find:

The formula for a⁵-b⁵ =?

Solution:

aⁿ - bⁿ = (a - b)(aⁿ⁻¹b⁰ + aⁿ⁻²b¹ +...+ a¹bⁿ⁻² + a⁰bⁿ⁻¹)

[x⁰ = 1]

aⁿ - bⁿ = (a - b)(aⁿ⁻¹ + aⁿ⁻²b +...+ abⁿ⁻² + bⁿ⁻¹)

for all positive integral values of n.

Here, n = 5.

So, a⁵ - b⁵ = (a - b)(a⁵⁻¹b⁰ + a⁵⁻²b¹ + a⁵⁻³b² + a¹b⁵⁻² + a⁰b⁵⁻¹)

a⁵ - b⁵ = (a - b)(a⁴ + a³b² + a²b² + ab³ + b⁴)

Therefore, the formula for a⁵-b⁵ is (a - b)(a⁴ + a³b² + a²b² + ab³ + b⁴).

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