Binomial Expansion (1+4x)^7: Guide for Correct Answer

[DeanBH]

(1+4x)^7 i need to fully expand.

il use (4c0) for 4 Ncr 0.


(4c0)1^4 + (4c1) 1^3 + 4x + (4c2) 1^2 4x^2 + (4c3) 1 + 4x^3 +
(4c4) 4x^4.

this gives the completely wrong answer.

i know this isn't the way your meant to do it, but i can't remember what's wrong here.

can someone tell me how to do this.. thanks :P

 

[HallsofIvy]

(1+4x)^7 i need to fully expand.

il use (4c0) for 4 Ncr 0.


(4c0)1^4 + (4c1) 1^3 + 4x + (4c2) 1^2 4x^2 + (4c3) 1 + 4x^3 +
(4c4) 4x^4.

this gives the completely wrong answer.

Yes, it does! For one thing you have have only 4th power while your problem says 7th powers. Is one of those a typo? The second difficulty is that "(4c1)1^3+ 4x". the 3rd power of 1 should be multiplied by the "4x", not added: (4c1)1^3(4x). Finally, it is "4x" that should be to each power, not just "x".
(1+ 4x)^4= (4c0)1^4+ (4c1)1^3(4x)+ (4c2)1^2(4x)^2+ (4c3)1(4x)^3+ (4c4)(4x)^4

i know this isn't the way your meant to do it, but i can't remember what's wrong here.

can someone tell me how to do this.. thanks :P