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Savatey [412]
3 years ago
8

Binomial expansion of (x+2)^4

Mathematics
1 answer:
N76 [4]3 years ago
4 0
The two terms are x and 2, thus, x+2 is a binomial.  We have to multiply the binomial by itself four times since it is raised to 4th power.

Let us multiply x+2 by itself using Polynomial Multiplication:

(x+2)(x+2) = x^2 + 4x + 4

Taking the result, let us multiply it again by a+b:

(x^2 + 4x + 4)(x+2) = x^3 + 6x^2 + 12x + 8

And again:

(x^3 + 6x^2 + 12x + 8)(x+2) = x^4 + 8x^3 + 24x^2 + 32x +16

The binomial expansion of (x+2)^4 is  x^4 + 8x^3 + 24x^2 + 32x +16
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