Question

Factor this radical expression. 50a^2-10ab/20a^3b^3

Answer 1

1)split into two fractions

`(50a^(2) )/(20a ^(3) b ^(3) )` -
`(10ab )/(20a ^(3) b ^(3) )`

2) cancel what you can on both sides

`(5)/(2ab ^(3) )` -
`(1)/(2a ^(2)b ^(2) )`

3) Make the denominators the same by cross multiplying and then put together as 1 fraction again

`(5a-b)/(2a ^(2)b ^(2) )`

Answer 2

remembe
(ax)/(bx)=(a/b)(x/x)=(a/b)1
find ones aka common factors and use distributive

top
50a^2-10ab
common facotrs is 10a
undistribute (ab+ac=a(b+c))
10a(5a-b)

bottom
20a^3b^3
see if 10a is also a common factor and undistribute that to cancel and make ones
10a(2a^2b^2)

now we have

`(10a(5a-b))/(10a(2a^(2)b^(3))`=
`(10a)/(10a)`
`(5a-b)/(2a^(2)b^(3))`