(192x^2y+72x^3)-(24rxy-9rx^2)
I need help factoring completely in groups and can you please show all your work thank you
192x^2y + 72x^3 = 24x^2(8y+3x)
24rxy - 9rx^2 = 3rx(8y-3x)
The only common factor I can see is 3x, so we have
3x(64xy+24x^2-8ry+3rx)
Not sure just where you're trying to go with this
Now, if the original had been without the parentheses,
(192x^2y+72x^3)-24rxy-9rx^2
then we would have had
24x^2(8y+3x)-3rx(8y+3x)
(24x^2-3rx)(3x+8y)
3x(8x-3r)(3x+8y)
To factor the given expression completely using the grouping method, follow these steps:
Step 1: First, identify the common factors shared by each term within each group separately. In this case, there are two groups: Group 1 consists of (192x^2y) and (72x^3), and Group 2 consists of (24rxy) and (-9rx^2).
Group 1 factors:
192x^2y = (2*96)xy = 2*12*8x*x*y = 24xxy
72x^3 = (2*36)x^2 = 2*12*3x^2*x = 24x^2*x
Group 2 factors:
24rxy = (3*8)rx*y = 3*4*2rxy = 12rxy
-9rx^2 = (-3*3)rx*x = -3*3rx^2
Step 2: Now, factor out the common factors from each group.
Factor Group 1:
24xxy - 24x^2*x = 24x^2y(x - x^2)
Factor Group 2:
12rxy - 3rx^2 = 3rx(4xy - x^2)
Step 3: After factoring each group separately, look for any common factors that can be factored out from both groups.
In this case, there are no common factors between (x - x^2) and (4xy - x^2).
Therefore, the completely factored expression is:
(24x^2y(x - x^2)) - (3rx(4xy - x^2))
Note that further factoring is not possible since there are no common factors between the terms in both groups.