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# Taking common factor from trinomial

Sal factors 4x⁴y-8x³y-2x² as 2x²(2x²y-4xy-1) by taking the greatest common factor. Created by Sal Khan and Monterey Institute for Technology and Education.

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• Could some one please drop some knowledge on me and help me factor 8x^3 - y^6 ???? do i need to cut it down to 8x^3 - 2y^3? this doesn't look right to me. Pre-reply thanks guys :)
• [I realize the post is quite old, but in case it helps:]

Note that you have a difference of cubes, which means you can use the well known, established pattern for factoring your binomial. See: <https://www.khanacademy.org/math/algebra/polynomials/dividing_polynomials/v/difference-of-cubes-factoring>

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Restate each term as a perfect cube and substitute for "a" and "b" (ignore the signs):

8x^3 - y^6:
a = (2x)^3 = 8x^3
b = (y^2)^3 = y^6

(2x - y^2)[(2x)^2 + (2x)(y^2) + (y^2)^2]

Which, when further simplified, yields Jason's answer:

(2x - y^2)(4x^2 + 2xy^2 + y^4)

One common mistake that catches me is mixing up exponentiation properties. For example: mixing up (a^b)^c = a^(b*c) with a^b * a^c = a^(b+c).
• Why is x^3 divided by x^2 just x?
• x^3 is the same as x*x*x, whilst x^2 is the same as x*x. Obviously if you multiply X^2 by x then its the same as x*x*x (x^3). In which case we can assume dividing x*x*x/x*x = x. Im sorry i couldn't give a better explanation but i hope that helps a little. also if you want proof. Lets say x= 10. we get 1000/100=10 wich is true. Watch the videos on exponents if you want more info.
• At ... I know this is right, I just need an explanation.

How does x^2 go into x^3 and x^4?
• 5 goes into 15, 3 times (5*3=15)
8 goes into 16, 2 times (8*2=16)
9 goes into 54, 6 times(9*6=54)
x^2 goes into x^3, x times (x^2 * x=x^3)
x^2 goes into x^4, x^2 times (x^2 * x^2 = x^4)
• why did sal multiply and divide 2x squared?
• It may not be the best way to describe/ think about it. Do you understand how 4x^4y can be rewritten as (2x^2)(2x^2y)? It's basically that thinking, and then using the method of (5x^2+4xy+6x) = x(5x+4y+6) If you don't get that relation try working n reverse and distribute the x. Factoring a lot of times can be thought of as reverse distributing. Does that help?
• why we have taken only smallest no.
• I'm assuming you meant the smallest number--we take the smallest number out of 2 , 4, and 8 because 2 is the largest number that can divide EACH of the numbers evenly. If we wanted to use 2, 4, or 8--or any number, really--we could, but it would make it more complicated because we would have fractions.
• I tried to do this for a question, and Khan Academy said I was incorrect, any tips?
(3b^5)+(15b^4)-(18b^7) = 3(b^5 + 5^4 - 6b^7)
• First, you lost the variable in the middle term of your answer.
Next, you need to factor out the greatest common factor. You found the numeric portion, however, you didn't look at the variables. The greatest common factor must include some number of b's because all the terms have b's.
Give it a try. If you still can't get the right answer, comment back.
• how would you factor 4a^2+12ab+9b^2?
• I commonly see in posts and comments, below, this symbol --that I've inclosed within quotation marks, " ^ ". It usually comes after a letter and before a number. Is this symbol used to express an exponent?
• yes, it is hard to write an exponent on a computer so the use the "^" symbol and then the number.
• How would we factor x^2+4x+3 then?