-125x^3y-75xy^2+100x^3y^3 factor help
i have used a number tree to get
25 xy is a factor of all terms.
-125x^3y -75xy^2 +100x^3y^3
= 25xy*(-5x^2 -3y +4x^2y^2)
cos2A=?
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To factor the expression -125x^3y - 75xy^2 + 100x^3y^3, we can look for common factors and try to rearrange terms to apply certain factoring techniques.
Firstly, let's look for any common factors among the three terms.
The coefficient of each term is divisible by 5, and each term contains at least one factor of x and y. Therefore, we can factor out the greatest common factor (GCF) of -125x^3y, -75xy^2, and 100x^3y^3, which is 25xy. This gives us:
25xy(-5x^2 - 3y + 4xy^2)
Now, let's focus on the remaining expression within the parentheses, -5x^2 - 3y + 4xy^2. We will try to further factor this expression.
Looking at the factors -5x^2, -3y, and 4xy^2, we need to identify any common factors or patterns that can be pulled out.
To simplify the process, let's rearrange the terms in the expression:
4xy^2 - 5x^2 - 3y
Now, let's take a closer look at the terms.
Notice that the first two terms, 4xy^2 and -5x^2, have a common factor of x. Therefore, we can factor out an x, resulting in:
x(4y^2 - 5x - 3y)
Now, let's focus on the remaining expression, 4y^2 - 5x - 3y. We will try to factor this further.
We can look for factors or patterns by grouping the terms. Let's pair the terms:
(4y^2 - 3y) - 5x
In the first group, we can factor out a common factor of y:
y(4y - 3) - 5x
Now, we can see that we have a common factor of (4y - 3) in both terms. Therefore, we can factor this out:
(4y - 3)(y - 5x)
Finally, we have factored the original expression as:
25xy(4y - 3)(y - 5x)
So, the final factored form is 25xy(4y - 3)(y - 5x).