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March 30, 2017

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Expand (1-6x)^4 (1+2x)^7 in ascending powers of x up to and includeing the terms in x^3.

  • maths - ,

    (1-6x)^4
    = 1^4 + 4*1^3(-6x)^1 + 6*1^2(-6x)^2 + 4(1^1(-6x)^3 + 1(-6x)^4
    = 1-24x+216x^2-864x^3+...

    (1+2x)^7 = 1+14x+84x^2+280x^3+...

    Now just work from the left

    1(1+14x+84x^2+280x^3)
    -24x(1+14x+84x^2+280x^3)
    +216x^2(1+14x+84x^2+280x^3)
    -864x^3(1+14x+84x^2+280x^3)

    ...

    1-10x-36x^2+424x^3+...

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