Mathematics: What is the binomial expansion of (x + 2y)7?

What is the binomial expansion of (x + 2y)7?

Ответ:

tonimgreen17p6vqjq

03.01.2022

Mathematics

x^7+14x^6y+84x^5y^2+280x^4y^3+560x^3y^4+672x^2y^5+448xy^6+128y^7

Step-by-step explanation:

Given: equation = (x + 2y)^7

Using binomial expansion which state that

$(a+b)^n=\sum {_{n}\textrm{C}_k a^{n-k}b^k}$

where a= x, b=2y, n=(0,1,2...,7), k =(0,1,2....,7)

Applying the binomial expansion

We get,

$\frac{7!}{(7-0)!0!} x^{7-0}(2y)^0+ \frac{7!}{(7-1)!1!} x^{7-1}(2y)^1+\frac{7!}{(7-2)!2!} x^{7-2}(2y)^2+\frac{7!}{(7-3)!3!} x^{7-3}(2y)^3+ \frac{7!}{(7-4)!4!} x^{7-4}(2y)^4+\frac{7!}{(7-5)!5!} x^{7-5}(2y)^5+\frac{7!}{(7-6)!6!} x^{7-6}(2y)^6+ \frac{7!}{(7-7)!7!} x^{7-7}(2y)^7$

solving this we get,

x^7+14x^6y+84x^5y^2+280x^4y^3+560x^3y^4+672x^2y^5+448xy^6+128y^7

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Ответ:

lilkit

18.07.2022

Mathematics

skdkekeirjejejsjsebdjhdb3rudhdh

Step-by-step explanation:

4urhebru4

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What is the binomial expansion of (x + 2y)7?

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