Factor Special Products: example 7.46

Factor: $36 x^{2} y - 48 x y + 16 y$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor: $8 x^{2} y - 24 x y + 18 y$ .

How did it go?

	$36 x^{2} y - 48 x y + 16 y$
Is there a GCF? Yes, 4y, so factor it out.	$4 y (9 x^{2} - 12 x + 4)$
Is this a perfect square trinomial?
Verify the pattern.
Factor.	$4 y {(3 x - 2)}^{2}$
Remember: Keep the factor 4y in the final product.
Check.
$4 y {(3 x - 2)}^{2}$
$4 y [{(3 x)}^{2} - 2 \cdot 3 x \cdot 2 + 2^{2}]$
$4 y {(9 x)}^{2} - 12 x + 4$
$36 x^{2} y - 48 x y + 16 y ✓$

	$36 x^{2} y - 48 x y + 16 y$
Is there a GCF? Yes, 4y, so factor it out.	$4 y (9 x^{2} - 12 x + 4)$
Is this a perfect square trinomial?
Verify the pattern.
Factor.	$4 y {(3 x - 2)}^{2}$
Remember: Keep the factor 4y in the final product.
Check.
$4 y {(3 x - 2)}^{2}$
$4 y [{(3 x)}^{2} - 2 \cdot 3 x \cdot 2 + 2^{2}]$
$4 y {(9 x)}^{2} - 12 x + 4$
$36 x^{2} y - 48 x y + 16 y ✓$