Maths Binomial Expansion Question Watch

Shopaholic94
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Hi, I'm having trouble with this question. Would anyone be able to help me work through it please:

If x is so small that terms of x^3 and higher can be ignored, expand the following (2x+3)(1+2x)^5
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dknt
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(Original post by Shopaholic94)
Hi, I'm having trouble with this question. Would anyone be able to help me work through it please:

If x is so small that terms of x^3 and higher can be ignored, expand the following (2x+3)(1+2x)^5
It's basically asking you to expand this up to the x^3 term. There are a few ways to do this. You can do it the long way and expand everything out and pick out what you need, but that'd take a long time.

Try expanding the power of 5 bracket up to the x^3 term first with your binomial expansion. You can ignore the higher terms because those powers would exceed x^3 and we're told we can discount them. And then see what happens when you multiply those terms by (2x+3)
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Lord dudek
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(Original post by Shopaholic94)
Hi, I'm having trouble with this question. Would anyone be able to help me work through it please:

If x is so small that terms of x^3 and higher can be ignored, expand the following (2x+3)(1+2x)^5
begin by expanding (1+2x)^5

Method 1 - using general binomial expansion formula

(note it is already in the form to use the general binomical expansion forumla: (1+ax^b)^n)

=1+(5)(2x)+(((5)(4)(2x)^2)/2)+(((5)(4)(3)(2x)^3)2*3)) sorry for all the brackets
=1+10x40x^2+80x^3

method 2 - using pascals triangle

(1+2x)^5

1 5 10 10 5 1
1 1 1 1 1 1
1 2x 4x^2 8X^3 16x^4 32x^5

=1 + 10x +40x^2 +80x^3.....

both methods work fine, however the gernal binomial expansion is particulary useful because you can use if for negative, and fractional powers.

after doing this all you need to do is:

(2x+3)(1 + 10x +40x^2 +80x^3) and expand, which you can do youself.
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