Question

What is the factored form of the expression over the complex numbers?

4x2+25y2




options-


a (2x+5iy)(2x−5iy)


b (2x−5y)(2x+5y)


c(2x+5iy)(2x+5iy)


d (2x−5iy)(2x−5iy)

Answer 1

the answer is A

Explanation:

Answer 2

The answer the factores over complex number of the expression
`(4x^(2) +25y^(2))`

a). (2x+5iy)*(2x-5iy)

Explanation:

`(2x+5iy)(2x-5iy)\\(2x*2x)+(2x*+5yi)+(-5yi*2x)+(5iy*5iy)`

Remember

`i=√(-1)\\i^(2)=-1`

Check:

`(4x^(2) -10xyi +10xyi -25 i^(2) *y^(2) )\\(4x^(2) -25* i^(2) *y^(2) )\\(4x^(2) -25 *(-1) *y^(2) )\\(4x^(2) + 25 y^(2) )`