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factoring

by JGaynor » Thu Apr 08, 2010 6:10 am
Hey everyone,

what are the common equations to factor that should be memorized...like (a+b)^2 = a^2 + b^2 + 2ab

I know every once in a while some people post the list in random posts but I can't find them...thank you!

Jason
Last edited by JGaynor on Thu Apr 08, 2010 8:20 am, edited 1 time in total.
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by thephoenix » Thu Apr 08, 2010 6:24 am
JGaynor wrote:Hey everyone,

what are the common equations to factor that should be memorized...like (x-y)^2 = (x+y)(x-y)

I know every once in a while some people post the list in random posts but I can't find them...thank you!

Jason
(x-y)^2 # (x-y)(x+y)
its = (x-y)(x-y)=x^2-2x+y^2

(a-b)^2;(a-b)^3;(a^3-b^3);a^2-b^2
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by eaakbari » Thu Apr 08, 2010 6:59 am
(a+b)^2 = a^2 + b^2 + 2ab

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

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

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

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

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



HTH
Last edited by eaakbari on Thu Apr 08, 2010 8:22 am, edited 1 time in total.
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by eaakbari » Thu Apr 08, 2010 7:00 am
JGaynor wrote:Hey everyone,

what are the common equations to factor that should be memorized...like (x-y)^2 = (x+y)(x-y)

I know every once in a while some people post the list in random posts but I can't find them...thank you!

Jason

Your above formula is stated wrong. The L.H.S is x^2 - y^2. Do edit it
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by JGaynor » Thu Apr 08, 2010 8:20 am
Thank you! Keep them coming if there any more....this helps a lot!
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by kevincanspain » Thu Apr 08, 2010 1:33 pm
How about a way to factor ax^2 + bx + c = 0 if the roots (solutions) are rational numbers?


Write (ax + p)(ax + q)/a where pq = ac and p+q = b


For example 6x^2 + x - 40

pq =240
p + q = -1

p= 15 q= -16


(6x + 15)(6x - 16)/6 =3(2x+5)(3x - 8)2 / 6

(2x+5)(3x - 8)


Another example:

24x^2 - 5x - 36

pq= 24(-36)= - (2^5)(3^3)
p+q = - 5

p= -2^5=-32 q=3^3= 27

(24x -32)(24x +27)/24
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by eaakbari » Fri Apr 09, 2010 12:32 am
Oh yes, great addition Kevin.
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by shashank.ism » Fri Apr 09, 2010 2:13 am
Really the property of quadratic equation i.e. for a quad. eq. ax^2 + bx + c = 0
sum of roots = -b/a
and product of roots = c/a

is very helpful and we can solve the problem very easily..
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