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C2 EDEXCEL, binomial expansion question.

Mixed excercise 5E.

12. the coefficient of x^2 is the binomial expansion of (2+kx)^8, where k is a positive constant, is 2800.

A) use algebra to calculate the value of k.
B) use your value ok k to find the coefficient of x^3 in the expansion.

Thanks before-hand :smile:

Reply 1

MichailZ

A)

2800x² = (8nCr2) x 2^6 * k²x²
2800 = 28 * 64 * k²
k² = (2800)/(28 * 64) = 25/16
∴ k = 5/4

B)

8nCr3 * 2^5 x (5/4)^3 = 3500

Hope this helps.

Michail

Reply 2

Dekota

yo_dude

12. the coefficient of x² is the binomial expansion of (2+kx)^8, where k is a positive constant, is 2800.

A) use algebra to calculate the value of k.
B) use your value k to find the coefficient of x^3 in the expansion.

(2+kx)^8 = 2^8 + (8).2^7.(kx) + (28).2^6.(kx)² + (56).2^5.(kx)³ +...

A) (28).2^6.(kx)²
...=> 1792k² = 2800
...=> k² = 1.5625
...=> k = 1.25

B) (56).2^5.(kx)³
...=> 1792k³ => 1792(1.25)³ = 3500

Reply 3

Dimez

a) Open up the brackets up to the x² sequence using the binomial formula in terms of k. Equate that to 2800 and solve accordingly.

b) Using your value of k from part a), use the formula again to calculate the coefficient of x³.

:smile:

Reply 4

yo_dude