SOLUTION: Please help me understand how to complete problems such as Factor completely: {{{ 9a^2 - 24ab + 16b^2}}} Thanks

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Question 42489: Please help me understand how to complete problems such as
Factor completely: +9a%5E2+-+24ab+%2B+16b%5E2
Thanks

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
If you need a detailed solution on how to factor trinomials such as this, see my three (3) recently posted Lesson Plans in algebra.com under the topic of Quadratic Equations:

"More Factoring in Living Color in Quadratic_Equations."
"Factoring Difference of Squares in Living Color in Quadratic_Equations."
"Factoring Trinomials in Living Color in Quadratic_Equations. "

To solve the current problem, +9a%5E2+-+24ab+%2B+16b%5E2 start with the first times first, which is probably 3a*3a
%283a_____%29%283a_____%29+

Next look at the last term, which has to be a 16b^2. This is probably a 4b*4b.
+%283a___4b%29%2A%283a___4b%29+

Next, since the last term is positive, the signs must be the SAME. Since the middle term is -24ab, the signs must be NEGATIVE.
+%283a-4b%29%2A%283a-4b%29+=+%283a-4b%29%5E2

R^2 at SCC