Question

Write 9− 16x⁴ as the product of two factors.

Answer 1

The two factors will be
`=(3+4x^2)\ and\ (3-4x^2)`

Explanation:

We have given the equation
`9-16x^4`

We know the algebraic equation
`a^2-b^2=(a+b)(a-b)`

As
`9-16x^4` can be written as
`3^2-(4x^2)^2`, as square of 3 is 9 and square of
`4x^2` is
`16x^4`

So
`9-16x^4=3^2-(4x^2)^=(3+4x^2)(3-4x^2)`

So the two factors will be
`=(3+4x^2)\ and\ (3-4x^2)`