Question 21916
<pre>factor completely over the integers:

121 - 64x<sup>2</sup> - 36y<sup>2</sup> + 96xy

I've tried pairing the integers in different ways and still
can't solve this.
Please help.

Thank you.
-------------------------------------------------------------------
<font size = 3>Sometimes pairing doesn't work and you have to try grouping 
three factors:

121 - 64x<sup>2</sup> - 36y<sup>2</sup> + 96xy

Interchange the last two terms

121 - 64x<sup>2</sup> + 96xy - 36y<sup>2</sup>

Factor -4 out of the last three terms

121 - 4(16x2 - 24xy + 9y2)

Factor the expression in the parentheses

121 - 4(4x-3y)(4x-3y)

This is now the difference of two perfect squares

11<sup>2</sup> - 2<sup>2</sup>(4x-3y)<sup>2</sup>

[11 - 2(4x-3y)][11 + 2(4x-3y)]

Remove the parentheses inside the brackets

[11-8x+6y][11+8x-6y]

Change the brackets to parentheses

(11-8x+6y)(11+8x-6y)

Edwin
AnlytcPhil@aol.com</pre>