32x^2y-64xy-4x^3y. When I factored out the GCF, I got 4. When I try to factor is completely, I got lost and confused. Can someone please help???
Your GCF is 4xy
32x^2y-64xy-4x^3y
= 4xy(8x - 16 - x^2)
(expand the answer to verify)
Of course, I'm here to help! Factoring expressions can sometimes be tricky, but don't worry, I'll guide you through the process step by step.
Let's start by looking at the expression again:
32x^2y - 64xy - 4x^3y
The first step is to see if there is a common factor among all the terms. In this case, you correctly identified the greatest common factor (GCF) as 4. To factor out the GCF, you divide each term by 4:
(4 * 8x^2y) - (4 * 16xy) - (4 * x^3y)
Now, let's simplify this to:
4(8x^2y) - 4(16xy) - 4(x^3y)
Next, we can further simplify by factoring out common factors from each term. Let's break down each term separately:
1. 4(8x^2y):
Here we have 4 multiplied by 8x^2y. To factor out common factors from 8x^2y, we need to identify the factors that appear in all terms. In this case, the factors are 2, x, and y. Therefore, we can rewrite this term as:
4 * (2 * 4 * x * x * y)
Simplifying further gives us:
4 * (2xy * 4x)
Now we have factored out the common factors from the first term.
2. -4(16xy):
In this term, we have -4 multiplied by 16xy. Again, we need to identify the factors that appear in all terms. The factors common to all terms are 4, x, and y. Rewriting this term gives us:
-4 * (4 * 4 * x * y)
Simplifying further:
-4 * (4xy)
Now we have factored the common factors from the second term.
3. -4(x^3y):
Finally, in the last term, we have -4 multiplied by x^3y. Once again, we identify the common factors as 4, x, and y. Rewriting this term gives us:
-4 * (x * x * x * y)
Simplifying further:
-4x^3y
We have now factored the common factors from the third term.
Putting it all together, we get:
4(2xy * 4x) - 4(4xy) - 4x^3y
This can be further simplified as:
8xy * 4x - 4 * 4xy - 4x^3y
Finally, we can factor out common factors again:
8xy * 4x - 16xy - 4x^3y
And that's the completely factored form of the expression.
I hope this explanation helps! If you have any further questions, feel free to ask.