Question

Kiran and Mai are trying to figure out if this equation is an identity, what do you think
and why?
(a - b)^4 = a^4 – 4a^3 b + 6a^²b^2 – 4ab^3 + b^4

Answer 1

Expanding the left side of the equation, it is found that since both sides are equal, yes, it is an identity.

An equality represents an identity if both sides are equal.

In this problem:

$(a - b)^4 = a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4$

Expanding the left side:

$(a - b)^2(a - b)^2 = a^4 - 4a^3b + 6a^2b^2 + 4ab^3 + b^4$

$(a^2 - 2ab + b^2)(a^2 - 2ab + b^2) = a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4$

$a^4 - 4a^3b + + 6a^2b^2 - 4ab^3 + b^4 = a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4$

Since both sides are equal, yes, it is an identity.

A similar problem is given at https://brainly.com/question/24866308