Question

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Answer 1

Answer:

Step-by-step explanation:

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.