I don't understand factoring in math at all. HELP!?

Question

Two problems I need to solve are (x^2)-6x+9 and (21x^2y)-(9xy^2)-(30y^3). The ^2 means squared and the ^3 means cubed.

Answer 1

the first is: (x-3)(x-3)
.....the trick for doing this one is what two numbers multiply to 9 and add to -6
second one: factor out a 3y to get : 3y(7x^2-3xy-10y^2) next u factor the inside to get (3y)(7x-10y)(x+y)....once again the trick is wat 2 numbers multiply to 10y^2 and add to 7xy...this one is a little tricker because u also have to take in account the 7 x

hope this helps

Answer 2

In general, you know that:

(x+y)(x-y) = x^2 - y^2

So, start with:

(x + _)(x - _)

and work with the common denominators of nine. Using FOIL, multiple your answer out to check. Fiddle with the plus and minus signs until you get the middle term you're looking for. Sometimes, guess and check is the only method to factor things out.

For the more complicated questions, look for a common term among all the terms. For example, in this equation, there's a "y" common to all three terms. Take that out of the equation, and set it to the side. You can also divide all numbers by "3", so take that out and place it next to the "y". Now, use the same approach as above to factor the rest. When you're done, don't forget to include the 3y as part of your factored equation.

Answer 3

Terms are things added or subtracted. Factors are things multiplied or divided together.
Dollar bills in your pocket are terms.
Taxes, tips and interest are factors.
The tree terms in (x^2)-6x+9 are
(x^2) (aka x * x)
-6x
9
They don't have any factors in common.

However, the whole mess can be made by multiplying two things together:
You're looking for two factors of two terms each, because that's the kind of problem your teacher is giving you lots of this semester. Like ( something + something) * ( something + something).
The term on the left (x^2) could come from (x something) * (x something)
The term on the right (9) could come from
(something + 3) * (something + 3) or
(something - 3) * (something - 3) or
(something + 1) * (something + 9) or
(something - 1) * (something - 9)

The term in the middle (-6x) would come from a combination of two of the above.
3x+3x=6x
-3x+ (-3x) = -6x (Yeah!)
1x+9x=10x
-1x+(-9x) = -10x

So (x-3)(x-3) = x^2-6x+9

Answer 4

okay x squared implies there's going to be 2 of them
and you have to find a number that adds to be -6 and multiplies to be 9
so you're numbers are going to be -3 and -3
so now you have (x-3)(x-3)

okay, the second one is also going to have a common denominator of 3
and all the numbers are multiplied by y
so you have 3y(7x^2-3xy-10y^2)

I hope this helps

Answer 5

the first is (x-3)^2 couse of the formula a^2-2ab+b^2=(a-b)^2

second 3y(7x^2-3xy-10y^2)