Finding C in expansion (1+cx) (1+x)^4

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Find c given that the expansion (1 + cx) (1 + x)^4 includes the term 22x^3.

Guest Oct 30, 2014

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Best Answer

+130511

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(1 + cx) (1 + x)^4

Expanding (1+ x)^4 we have

(1 + 4x + 6x^2 + 4x^3 + x^4)

So (1 + cx)(1 + 4x + 6x^2 + 4x^3 + x^4) produces two x^3 terms, i.e. 4x^3 and 6cx^3

So

4 + 6c = 22 subtract 4 from both sides

6c = 18 divide both sides by 6

c = 3

CPhill Oct 30, 2014

1⁺⁰ Answers

+130511

+5

Best Answer

(1 + cx) (1 + x)^4

Expanding (1+ x)^4 we have

(1 + 4x + 6x^2 + 4x^3 + x^4)

So (1 + cx)(1 + 4x + 6x^2 + 4x^3 + x^4) produces two x^3 terms, i.e. 4x^3 and 6cx^3

So

4 + 6c = 22 subtract 4 from both sides

6c = 18 divide both sides by 6

c = 3

CPhill Oct 30, 2014

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