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Binomial Expansion help

If x is so small that terms of x^3 and higher can be ignored, show that:

(2 + x)(1 - 3x)^5 is approx. equal to 2 - 29x + 165x^2

Thank you for any help that can be given
Reply 1
Avatar for john !!
john !!
14
expand the right bracket upto terms in x^3, then multiply that by (2+x), and then remove the term in x^4.
Unparseable latex formula:

{\fs{4} (2+x)(1-3x)^5 \\ \, \\[br]= \ (2+x)(1^5 + 5(-3x) + \frac {5(4)(-3x)^2}{2!}) \\ \, \\[br]= \ (2+x)(1-15x + 90x^2) \\ \, \\[br]= \ (2 - 30x +180x^2 + x - 15x^2 +90x^3) \\ \, \\[br]= \ 2 - 29x + 165x^2

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