10xy-15x^2= 5xy(2x-3)factor out GCF
I can't decide if you want to factor the equation 10xy-15x^2= 5xy(2x-3) or if you
say the GCF of 10xy-15x^2 is 5xy(2x-3)
if it is the latter than the GCF of
10xy - 15x^2 is either 5x or (2y - 5x)
depending on the values of x and y.
if you want to factor the equation, then ...
10xy-15x^2 - 5xy(2x-3) = 0
10xy-15x^2 - 10x^2y + 15xy = 0
25xy - 10x^2y = 0
5xy(5 - 2x) = 0
To factor out the greatest common factor (GCF) from the given expression, we need to identify the common factors shared by all the terms. Let's break down the expression step-by-step:
10xy - 15x^2 = 5xy(2x - 3)
First, let's examine the coefficients. The coefficients for the terms 10xy and 15x^2 are 10 and 15, respectively. Both 10 and 15 are divisible by 5, so we can factor out 5.
5(2xy - 3x^2) = 5xy(2x - 3)
Next, let's look at the variables. The variables x and y are present in both terms. However, we can see that the term (2xy - 3x^2) does not have any common factors other than x. Thus, we can factor out x from the term to obtain:
5x(y - 3x) = 5xy(2x - 3)
Now, we have factored out the greatest common factor (GCF) of the given expression. The factored form is:
5xy(2x - 3)