Question

What is the factored form of the expression over the complex numbers? 4x2+25y2?

Answer 1

The factored form is 25y^2 + 8 if the 2 was supposed to be an exponent.

Answer 2

Answer:

$(2x+5iy)(2x-5iy)$

Step-by-step explanation:

If a and b are two positive numbers, then

$a^2+b^2=(a+ib)(a-ib)$                .... (1)

The given expression is

$4x^2+25y^2$

It can be rewritten as

$2^2x^2+5^2y^2$

Using distributive property of exponent we get

$(2x)^2+(5y)^2$                 $[\because a^mb^m=(ab)^m]$

Using formula (1) we get

$(2x+5iy)(2x-5iy)$                 $[\because a^mb^m=(ab)^m]$

Therefore, the factored form of the given expression is $(2x+5iy)(2x-5iy)$ .