How do you use the binomial series to expand ${(1 + x)}^{4}$ $(1 + x)^4$ ?

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How do you use the binomial series to expand ${(1 + x)}^{4}$ $(1 + x)^4$ ?

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Answer 1 · 2016-02-01T08:48:45

Use the pascal's triangle to find the answer easily: enter image source here

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$\to {(a + b)}^{4} = 1 a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + 1 b^{4}$ $rarr(a+b)^4=1a^4+4a^3b+6a^2b^2+4ab^3+1b^4$

$\to {(1 + x)}^{4} = 1 {(1)}^{4} + 4 (1^{3}) x + 6 (1^{2}) x^{2} + 4 (1) x^{3} + 1 (x^{4}) = 1^{4} + 4 x + 6 x^{2} + 4 x^{3} + 1 (x^{4}) = 1 + 4 x + 6 x^{2} + 4 x^{3} + x^{4}$ $rarr(1+x)^4=1(1)^4+4(1^3)x+6(1^2)x^2+4(1)x^3+1(x^4)=1^4+4x+6x^2+4x^3+1(x^4)=1+4x+6x^2+4x^3+x^4$

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How do you use the binomial series to expand ${(1 + x)}^{4}$ $(1 + x)^4$ ?

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