# How do you use the Binomial Theorem to expand (x + 1)^4?

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#### Explanation

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#### Explanation:

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13
May 31, 2016

${\left(x + 1\right)}^{4} = {x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4 x + 1$

#### Explanation:

To use the binominal theorem we must know what Pascals triangle is because it gives us the binominal coefficients.

Note that the top "1" is considered row no 0 by convention.
So to get our coefficients we go to the 4th row and get our seqence of $1 , 4 , 6 , 4 , 1$.

that means that we will have to multiply each x with the corresponding value from the sequence.

In our answer we can see this:

${\left(x + 1\right)}^{4} = {x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4 x + 1$

All the numbers are the same as our sequence (but the "1's" have been removed in the answer since ${x}^{4} \cdot 1 = {x}^{4}$ and $1 \cdot 1 = 1$

the next thing to do is to raise our $y - v a l u e$ to the power of $\frac{n}{0} , \frac{n}{1} , e t c$ until we get to $\frac{n}{n}$ but since ${1}^{n} = 1$ we don't need to do anything except for the last row where we have our $+ 1$.

It all becomes much more evident if we exchange the $1$ for $y$
giving us:

${\left(x + y\right)}^{4} = {x}^{4} + 4 {x}^{3} y + 6 {x}^{2} {y}^{2} + 4 x {y}^{3} + {y}^{4.}$

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