1. Factorize

Suppose I have to factorize the following expression:

$\displaystyle x^2 + 14x + 33$

This is how I do it:

$\displaystyle x^2 + 11x + 3x + 33$ (because 11 + 3 = 14 & 11 * 3 = 33)
$\displaystyle x(x + 11) + 3(x + 11)$
$\displaystyle (x + 11)(x + 3)$

But how do I factorize the following 3 expressions?

$\displaystyle x^2 - 1 - 2y - y^2$

$\displaystyle 4(x - y)^2 - 12(x - y) + 9$

$\displaystyle 81(x + 1)^2 + 90(x + 1)(y + 2) + 25(y + 2)^2$

Thanks,

Ron

2. Originally Posted by rn5a
Suppose I have to factorize the following expression:

$\displaystyle x^2 + 14x + 33$

This is how I do it:

$\displaystyle x^2 + 11x + 3x + 33$ (because 11 + 3 = 14 & 11 * 3 = 33)
$\displaystyle x(x + 11) + 3(x + 11)$
$\displaystyle (x + 11)(x + 3)$

But how do I factorize the following 3 expressions?

$\displaystyle x^2 - 1 - 2y - y^2$

$\displaystyle 4(x - y)^2 - 12(x - y) + 9$

$\displaystyle 81(x + 1)^2 + 90(x + 1)(y + 2) + 25(y + 2)^2$

Thanks,

Ron
Q1 It's the same as x^2 - (y + 1)^2 ....

Q2 4a^2 - 12a + 9 = (2a - 3)^2 ....

Q3 81a^2 + 90ab + 25b^2 = (9a + 5b)^2 ....