Find the first three terms of the binomial expansion of (3 + 6x)^(1/2).
To find the binomial expansion of this expression we need to use a formula. The formula states that for expressions of (1 + x)n it can be written as: 1 + nx + (n(n-1)x2)/2 ...
As our initial expression does not contain a "1" we need to manipulate it first. Remove a factor of 3 from our expression, taking care to keep the power the same, giving " 31/2(1 + 2x)1/2 ". From here we can substitute in our values, to give a binomial expansion of 31/2(1 + x - x/2). This can further be simplified by bringing the factor back into the bracket.
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