Factor each trinomial, if possible. See Examples 3 and 4. (a-3b)^...

Question

Factor each trinomial, if possible. See Examples 3 and 4. (a-3b)^2-6(a-3b)+9

Accepted Answer

Hey, everyone here, we are asked to factor the following polynomial where we have the quantity of three U minus V squared minus 18 times the quantity of three U minus V plus 81. Now, our first step in factoring this expression is to recall our formula for a perfect square try no meal, which tells us that X squared minus two X Y plus Y squared is equal to the quantity of X minus Y squared. Now, all we have to do is compare our formula to our given expression to find our values for X and Y. So from our formula, we see that our first term is X squared. So we can look our first term in our given expression. And we see that X is going to be the square root of our first term. So X is the square root of the quantity of three U minus V squared, which simplifies to just the quantity of three U minus V. And now we can move on to finding our value for Y while we see from the formula that Y squared is our third term. So we can look at the third term of our given expression, which is 81 which tells us that why is going to be the square root of 81 which is just nine. And now we have found our values for X and Y. So we can go ahead and just plug them into the left hand side of our formula. So we have the quantity of three U minus V squared minus two times the quantity of three U minus V times nine plus nine squared. And now we can factor simplify this expression. And, and we see that we have the quantity of three U minus V squared minus 18 times the quantity of three U minus V plus 81. And now we see that the simplified expression here is equivalent to our given expression. So we know that the left hand side of our formula is equivalent to our given expression, which tells us that our expression is equal to the factored form here, which is the quantity of X, which again is three U minus V minus Y, which we know we have minus nine. And then we take this quantity and square it. And with this, we have found our factored form of our original expression which is answer choice B Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Factor each trinomial, if possible. See Examples 3 and 4. (a-3b)^2-6(a-3b)+9

Key Concepts

Factoring Trinomials

Perfect Square Trinomials

Completing the Square

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