Question

Explain the relationship between the polynomial identities: x^2 − 1 = (x +1)(x − 1) and x^2 − a^2 =(x − a)(x +a).

Answer 1

Answer:

So these two equation can be related by identity $x^2-a^2=(x+a)(x-a)$

Step-by-step explanation:

We have given equation $x^2-1=(x+1)(x-1)$

And $x^2-a^2=(x+a)(x-a)$

We know the algebraic identity $a^2-b^2=(a+b)(a-b)$

From this identity

$x^2-1$ can be written as (x+1) (x-1)

And using same identity $x^2-a^2$ can be written as $(x-a)(x-b)$

So these two equation can be related by identity $x^2-a^2=(x+a)(x-a)$