Question

a⁴+b⁴=?
Please someone tell me the Formula

Answer 1

Answer:

$a^4+b^4=(a+b)(a^{3}-a^{2}b+ab^2-b^3)$

Step-by-step explanation:

Fromula used:

$a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}b^2+..........+(-b)^{n-1})$

The expansion of $a^4+b^4$ is got by putting n=4 in the above formula.

$a^4+b^4=(a+b)(a^{4-1}-a^{4-2}b+a^{4-3}b^2-a^{4-4}b^3)$

$a^4+b^4=(a+b)(a^{3}-a^{2}b+a^{1}b^2-a^{0}b^3)$

$a^4+b^4=(a+b)(a^{3}-a^{2}b+ab^2-b^3)$

Answer 2

Answer:

$(a^2 +\sqrt{2}ab+ b^2 )(a^2 -\sqrt{2}ab+ b^2 )$

Step-by-step explanation:

$a^4 + b^4 = (a^2)^2 + (b^2)^2$

∵  (x + y)² = x² + 2xy + y² ⇒ x² + y² = (x + y)² - 2xy,

$\implies a^4 + b^4 = (a^2 + b^2)^2 - 2a^2b^2$

$=(a^2 + b^2)^2 - 2a^2b^2$

$=(a^2 +b^2)^2 - (\sqrt{2}ab)^2$

By using x² - y² = (x + y)(x-y),

We get,

$a^4 + b^4 = (a^2 + b^2 +\sqrt{2}ab)(a^2 + b^2 -\sqrt{2}ab)$

Or

$a^4 + b^4 = (a^2 +\sqrt{2}ab+ b^2 )(a^2 -\sqrt{2}ab+ b^2 )$