Factorization: Advanced

[Guest]

I go to Kumon and I have worksheets on which I don't understand.
I know how to do the basic factorization but this is was different. I need help on these and it is alot.

I 63a:

2. 3x(x-2y)^2-(x-2y)^3=

3. 2x^2(x+1)^2-12x(x+1)=

4. x(a+b)+x(a+c)=

5. x(2a+3b+x(a+3b)=

6. x(a+2b)+x(a+2c)=

7. (a-b)(x^2-5)-(a-b)(3x+5)=

I 65:

1. 9y^2-(2x-y)^2=

2. (x-3y)^2-(y-x)^2=

3. (3x-y)^2-(y-x)^2=

4. 25x^2-(x+2y+4z)^2=

I really need to know how to do this please and get the answers tonight so I can have it done tomorrow when I go to Kumon.

 

[stapel]

The point of Kumon is that you learn in the lesson they provide, and then you practice on the take-home sheets. Giving you the answers to the take-home sheets won't help you finish the timed exam in your Kumon session. (My kid has done Kumon, so I have some familiarity with how pointless it would be to try to cheat their system.)

Are you utterly lost, so you don't even know how to multiply out the squares? Or are you just not sure of your final answers? Or something else?

Please specify where you are having trouble. And please mention the trouble to your Kumon examiner, so corrected placement may be considered.

Thank you.

Eliz.

 

[galactus]

2. 3x(x-2y)^2-(x-2y)^3=

Here's a freebie. The best way to learn to factor is to do it.

\(\displaystyle \L\\3x(x-2y)^{2}-(x-2y)^{3}\)

Factor out \(\displaystyle \L\\(x-2y)^{2}\):

\(\displaystyle \L\\(x-2y)^{2}(3x-(x-2y))\)

\(\displaystyle \L\\(x-2y)^{2}\underbrace{(2x+2y)}_{\text{factor out 2}}\)

\(\displaystyle \H\\2(x+y)(x-2y)^{2}\)

There......