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# C1 Polynomials help! Watch

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1. 10. a) Find the first three terms in the expansion of (1+2x)^10

I thought it might be 2x^10 + 20x^9 + 90x^9 but I'm not sure.

b) Use the substitution x = 0.01 and your answer to (a) to find an approximate value for 1.02^10. Give your answer to an appropriate number of decimal places.

2. (Original post by yesineedhelp)
10. a) Find the first three terms in the expansion of (1+2x)^10

I thought it might be 2x^10 + 20x^9 + 90x^9 but I'm not sure.

b) Use the substitution x = 0.01 and your answer to (a) to find an approximate value for 1.02^10. Give your answer to an appropriate number of decimal places.

You need to use the binomial theorem/expansion or whathever you may call it. Part b will follow on from there.
3. Question 1a) (1+2x)^10

=(10c0 *1) + (10c1 * 1 * 2x) + (10c2 * 1 * 4x^2)

=1 + (10 * 1 * 2x) + (45 * 1 * 4x^2)

= 1 + 20x + 180x^2

Question 1b)

put 0.01 as x into my equation.

i think this is right?

M-G-C-E
4. (Original post by yesineedhelp)
10. a) Find the first three terms in the expansion of (1+2x)^10

I thought it might be 2x^10 + 20x^9 + 90x^9 but I'm not sure.

b) Use the substitution x = 0.01 and your answer to (a) to find an approximate value for 1.02^10. Give your answer to an appropriate number of decimal places.

use binomial expansion:
(1+x)^n
x=2x
n=10

then use formula - 1 +(n)(x) +(n)(n-1)(x)^2/2! +(n)(n-1)(n-2)(x)^3/3! and so on....

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Updated: November 28, 2010
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