How do you multiply (x - 1)^2?

Mar 14, 2018

${x}^{2} - 2 x + 1$

Explanation:

This is a fixed identity, these types of expressions, knowing the theory behind them, can be multiplied easily without any calculations.

For example, let's say you have the expression ${\left(x + y\right)}^{2}$
It becomes: ${x}^{2} + 2 x y + {y}^{2}$

If you have ${\left(x - y\right)}^{2}$
It becomes: ${x}^{2} - 2 x y + {y}^{2}$

You can see the pattern, you can learn it by heart, it is always the same in these cases.

But to explain you why the result is what it is:

${\left(x - 1\right)}^{2}$
$\left(x - 1\right) \cdot \left(x - 1\right)$
$x \cdot x - 1 \cdot x - 1 \cdot x - 1 \cdot \left(- 1\right)$
${x}^{2} - x - x + 1$
${x}^{2} - 2 x + 1$