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1986-4ii (1 Viewer)
- Thread starter bmn
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Monsterman
Member
factorise to (a+2)(a+1)
((a+2)(a+1))^6
(a+2)^6 find the coefficient a^4 of that
(a+1)^6 same as above sentence
times them together.. gg
((a+2)(a+1))^6
(a+2)^6 find the coefficient a^4 of that
(a+1)^6 same as above sentence
times them together.. gg
biopia
WestSyd-UNSW3x/week
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I'll expand on what the above poster is saying =]
Obviously, it is easy to factorise so
(a²+3a+2)⁶ ≡ (a+1)⁶(a+2)⁶
Expanding the RHS you will get:
[⁶C₀a⁶ + ⁶C₁a⁵ + ⁶C₂a⁴ + ⁶C₃a³ + ⁶C₄a² + ⁶C₅a + ⁶C₆][⁶C₀a⁶ + 2⁶C₁a⁵ + 4⁶C₂a⁴ + 8⁶C₃a³ + 16⁶C₄a² + 32⁶C₅a + 64⁶C₆]
Then, you have to isolate the terms that will multiply to give you something to the power of four and add them, so
⁶C₂a⁴.64⁶C₆ + ⁶C₃a³.32⁶C₅a + ⁶C₄a².16⁶C₄a² + ⁶C₅a.8⁶C₃a³ + ⁶C₆.4⁶C₂a⁴
Which, if I'm not mistaken, is 2005a⁴.
Bear in mind though, that I didn't have my scientific calculator with me, so I wrote up pascals triangle to get the values of those combinations, and did all multiplication on paper lol. If that value is incorrect, I am sure the expression is correct, and can be calculated accordingly.
Hope that helps!
=]
Obviously, it is easy to factorise so
(a²+3a+2)⁶ ≡ (a+1)⁶(a+2)⁶
Expanding the RHS you will get:
[⁶C₀a⁶ + ⁶C₁a⁵ + ⁶C₂a⁴ + ⁶C₃a³ + ⁶C₄a² + ⁶C₅a + ⁶C₆][⁶C₀a⁶ + 2⁶C₁a⁵ + 4⁶C₂a⁴ + 8⁶C₃a³ + 16⁶C₄a² + 32⁶C₅a + 64⁶C₆]
Then, you have to isolate the terms that will multiply to give you something to the power of four and add them, so
⁶C₂a⁴.64⁶C₆ + ⁶C₃a³.32⁶C₅a + ⁶C₄a².16⁶C₄a² + ⁶C₅a.8⁶C₃a³ + ⁶C₆.4⁶C₂a⁴
Which, if I'm not mistaken, is 2005a⁴.
Bear in mind though, that I didn't have my scientific calculator with me, so I wrote up pascals triangle to get the values of those combinations, and did all multiplication on paper lol. If that value is incorrect, I am sure the expression is correct, and can be calculated accordingly.
Hope that helps!
=]