Question

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

121x2+36y2




(11x+6y)(11x−6y)

(11x+6iy)(11x−6iy)

(11x−6iy)(11x−6iy)

(11x+6iy)(11x+6iy)

Answer 1

(11x + 6iy)(11x - 6iy)

using the difference of squares identity

a² - b² = (a - b)(a +b)

a² + b² = (a - bi )(a + bi)

121x² = ( 11x)² ⇒ a = 11x and 36y² = (6y)² ⇒ b = 6y

121x² + 36y² = (11x - 6iy)(11x + 6iy)

Answer 2

121x² + 36y²

= 121x² - (-36y²) Notice that the first and last term are perfect squares.

= (11x - 6iy)(11x + 6iy) So, you can factor using the difference of squares.

Answer: B