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Thread: Factoring with exponents

  1. #1
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    Factoring with exponents

    The question was this: (1+x)^1/2 + (1+x) ^3/2

    I worked it out as follows: = (1+x)^1/2 + (1+x)^1/2(1+x)^1 then factoring + sqrt 1+x ( 1 +(1+x))

    However, the answer was: (2+x)(1+x)^1/2 which i can't get my head around!-Help much appreciated (step by step if possible) -many thanks.
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  2. #2
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    Re: Factoring with exponents

    Quote Originally Posted by Simonsky View Post
    The question was this: (1+x)^1/2 + (1+x) ^3/2

    I worked it out as follows: = (1+x)^1/2 + (1+x)^1/2(1+x)^1 then factoring + sqrt 1+x ( 1 +(1+x))

    However, the answer was: (2+x)(1+x)^1/2 which i can't get my head around!-Help much appreciated (step by step if possible) -many thanks.
    $(1+x)^{1/2} + (1+x) ^{3/2}=(1+x)^{1/2}\left(1 + (1+x) ^{1}\right)=(1+x)^{1/2}\left(2+x\right)$
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  3. #3
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    Re: Factoring with exponents

    Hey, thanks - I just realised I'd got it right but just used an untidy notation! proves the point that (as someone famous said) 'maths is the art of saying the same thing in different ways.'
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  4. #4
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    Re: Factoring with exponents

    u = 1+x

    u^(1/2) + u^(3/2) = u^(1/2) + u^(2/2) * u^(1/2)
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