Question

Factor 4x²y⁴ − 25x⁴z⁶

Answer 1

the factor will be
`(2xy^2+5x^2z^3)(2xy^2-5x^2z^3)`

Explanation:

We have given the expression
`4x^2y^4-25x^4z^6`

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

`4x^2y^4-25x^4z^6` can be written as
`4x^2y^4-25x^4z^6=(2xy^2)^2-(5x^2z^3)^2`

Now using the above identity
`(2xy^2)^2-(5x^2z^3)^2=(2xy^2+5x^2z^3)(2xy^2-5x^2z^3)`

So the factor will be
`(2xy^2+5x^2z^3)(2xy^2-5x^2z^3)`