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Given the expression (5−4x)4
Write out the full binomial expansion:
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The binomial series expansion for an expression of the form (a+bx)n where n is a Natural number is given by:
(a+bx)n=(n0)(a)n(bx)0+(n1)(a)n−1(bx)1+(n2)(a)n−2(bx)2+...+(nk)(a)n−k(bx)k+...+(nn)(a)0(bx)n
In this example n=4, a=5 and b=−4.
So the binomial series expansion is:
54+(41)×54−1×(−4x)1+(42)×54−2×(−4x)2+ ... + (44)×54−4×(−4x)4
=625+2400x2−2000x−1280x3+256x4
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