(1-2x)^4(2x+x)^5 term containing x^3 | Mathematics | Page 1

pulsar yoke Oct 2, 2024, 3:10 AM

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(1-2x)^4(2x+x)^5 term containing x^3

flint boneBOT Oct 2, 2024, 3:10 AM

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rough trench Oct 2, 2024, 3:16 AM

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For clarification, is the problem to find the coefficient of the x^3 term?
And is the expression expressed correctly? I am guessing the expression is probably:
[ (1-2x)^4 ] [(2x + x)^5]

Seems strange? We can immediately combine (2x + x) into 3x to simplify the problem.

pulsar yoke Oct 2, 2024, 3:19 AM

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[ (1-2x)^4 ] [(2x + x)^5] yes this is correct

rough trench Oct 2, 2024, 3:23 AM

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are you familiar with binomial theorem? This would make things quicker

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because of the second term:
(2x + x)^5 = (3x)^5 = 243*x^5
make sense?

pulsar yoke Oct 2, 2024, 3:35 AM

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yes

rough trench Oct 2, 2024, 3:38 AM

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if we expand the first term (1-2x)^4 = (1 - ........)*(243x^5)
which means?

native grove Oct 2, 2024, 5:29 AM

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you only need the terms up to x^3 as well you don't have to calculate the full binomial expansion

blissful sonnet Oct 2, 2024, 4:10 PM

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#(1-2x)^4(2x+x)^5 term containing x^3