Question

If you are a Brilliant what is the formula for a4+b4

Answer 1

Answer:

Lets see….what you asked is formula for a^4 + b^4.

Step-by-step explanation:

Now I am Math major, and as far as I speak of algebraic expressions, i have learnt that algebraic expansions or factorization are closely related. So expansion of one is always considered as factorization of the other. They are vice versa.

So no, coming to your question… you mean to say that factorization or expansion of a^4 + b^4

As far as algebraic formulae are concerned, there is expansion formulas as below:-

(a+b) ^2 = a^2 + 2ab +b^2.

(a=b)^2 = a^2 – 2ab +b^2.

(a^2) – (b^2) = (a+b) (a-b)

But no expansion for (a^2) + (b^2) as it is only equal to as belo.

a^2 + b^2 = (a+b) (a+b) = a(a+b) + b (a+b) = a^2 + ab +ba + b^2 = a^2 + 2ab + b^2.

So now to your question….

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

= [(a^2) + (b^2)] [(a^2) + (b^2)] = a^4 + 2 (a^2)(b^2) + b^4

     = a^4 + 2a^2b^2 + b^4.

Answer 2

Answer:

$Formula \:for \: a^{4}+b^{4}$

=$\left(a^{2}+b^{2}\right)^{2}-2a^{2}b^{2}$

Or

=$\left(a^{2}-b^{2}\right)^{2}+2a^{2}b^{2}$

Step-by-step explanation:

$Formula \: for\:a^{4}+b^{4}$

=$\left(a^{2}+b^{2}\right)^{2}-2a^{2}b^{2}$

Or

=$\left(a^{2}-b^{2}\right)^{2}+2a^{2}b^{2}$

/* By algebraic identities:

i ) (x+y)² = x²+2xy+y²

ii) (x-y)² = x²-2xy+y² */

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