Expert: Ahmed Salami - 8/22/2010

Question
can u please help me complete the square for this...i keep getting stuck.

x^2 - 2x - 4y^2 - 16y - 15

thanks :)

Answer
Hi Heather,
x² - 2x - 4y² - 16y - 15 = (x² - 2x) - (4y² + 16y) - 15
                                           = [(x² - 2x + 1) - 1] - [(4y² + 16y + 16) - 16] - 15
                                           = (x² - 2x + 1)  - (4y² + 16y + 16) - 1 + 16 - 15
                                           = (x - 1)² - (2y + 4)²
Using the identity; A² - B² = (A + B)(A - B), the expression becomes
[(x - 1) + (2y + 4)][(x - 1) - (2y + 4)]
= (x + 2y + 3)(x - 2y - 5)

I hope its what you're looking for.

Regards