more factoring?

Question

i cant get this factoring stuff

1. ax-ay +x^2 -xy

2. 18x^3 -36x^2

3. 8m^4n - 16mn^4

4. 5a^2 -125?

Answer 1

1. ax-ay +x^2 -xy
a(x-y)+x(x-y)
(a+x)(x-y)

2. 18x^3 -36x^2
18x^2(x-2)

3. 8m^4n - 16mn^4
8mn(m^3-2n^3)

4. 5a^2 -125?
5(a^2-25)
5(a-5)(a+5)

Answer 2

1. (ax-ay)(+x^2 -xy) Bracket the first two terms then the last two
a(x-y) + x( x-y) Take out the common factor in each

2. 18x^3-36x^2
18x^2 ( x-2) Take out the common factors

3. 8m^4n- 16mn^4
8( 4m^n -2n^4)

4. 5( a^2 -25)

Answer 3

Factor out the common variables, and then reassess the problem:

1)a(x - y) + x(x - y) = (a + x)(x - y)

2) 18x^2(x-2)

3) 8mn(m^3 - 2n^3)

4) 5(a^2 - 25) = 5(a + 5)(a - 5)

Answer 4

an example for the second one: you have to find a number that is common to both numbers. What number can you divide 18 and 36 by? it would be 18. And then you can take out 2 x's from both terms.

Then you would write this: 18x^2(x-2) Because when you distribute (multiply both terms by 18 and x^2,) you get the same question back...18^3-36^2.

Answer 5

When factoring, take out the greatest common factor:

1)
The first two terms have a common 'a' term and the last two terms have a common 'x' term. Therefore, the factoring is:

a(x-y) + x(x-y)

You can take the factoring by one more step because both these terms have a common (x-y) term. Pull that out and you get:

(a+x)(x-y)
--------------------
2)
Both terms have a common term of '18x^2'. Pull that out and you get:

18x^2(x-2)
-------------------
3)
Both terms have a common term of '8mn'. Pull that out and you get:

8mn(m^3-2n^3)
-----------------
4)
Both terms have a common term of '5'. Pull that out and you get:

5(a^2-25).

You can take the factoring one more step because you see that the paranthesis is composed of a perfect square of the form (a-b)(a+b) = a^2 - b^2

Therefore, the complete factoring is:

5(a+5)(a-5)
---------------

Hope this helps

Answer 6

ax-ay+x^2-xy
a(x-y) +x(x-y)
(a+x)(x-y)

18x^3-36x^2
18x^2(x-2)

8m^4n -16mn^4
8mn(m^3-2n^3)

5a^2 -125
5(a^2-25)
5(a-5)(a+5)