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(2x+3y+4z) to the 3rd power

  • math -

    There is no easy rule, because there are many terms.
    The following identity could help:
    (a+b+c)^3
    =c^3+3bc^2+3ac^2+3b^2c+6abc+3a^2c+b^3+3ab^2+3a^2b+a^3
    So substitute 2x for a, 3y for b and 4z for c. Do not forget that a^2 would mean (2x)^2=4x^2, a^3 would mean (2x)^3=8a^3 and so on.

    A good way to check your work is to add up the coefficients, they should equal (2+3+4)^3 = 729.

  • math -

    very patiently expand
    (2x + 3y + 4z)(2x + 3y + 4z)(2x + 3y + 4z)
    = ....

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