# Can you expand (x-1)^4 ?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

14
Aug 26, 2017

${x}^{4} - 4 {x}^{3} + 6 {x}^{2} - 4 x + 1$

#### Explanation:

We need to expand ${\left(x - 1\right)}^{4}$. Using Pascal's triangle , we know that the coefficients of each progressive terms are: $1$ $4$ $6$ $4$ $1$.

We also know from the binomial theorem that when we perform an expansion of ${\left(a + b\right)}^{n} , n \in {\mathbb{Z}}^{+}$, the exponent of $a$ in each term decreases from $n$ to $0$ and the exponent of $b$ in each term increases from $0$ to $n$.

In this expansion, $x$ has a positive coefficient, so the sign will stay the same, but $- 1$ will have a sign change for every alternating term.

Bearing all of this in mind,

${\left(x - 1\right)}^{4}$
$= 1 {\left(- 1\right)}^{0} {x}^{4} + 4 {\left(- 1\right)}^{1} {x}^{3} + 6 {\left(- 1\right)}^{2} {x}^{2}$
$+ 4 {\left(- 1\right)}^{3} {x}^{1} + 1 {\left(- 1\right)}^{4} {x}^{0}$

$= {x}^{4} - 4 {x}^{3} + 6 {x}^{2} - 4 x + 1$

• 12 minutes ago
• 13 minutes ago
• 14 minutes ago
• 15 minutes ago
• 4 minutes ago
• 5 minutes ago
• 6 minutes ago
• 10 minutes ago
• 12 minutes ago
• 12 minutes ago
• 12 minutes ago
• 13 minutes ago
• 14 minutes ago
• 15 minutes ago