Algebra Examples

$(x - 1) (x - 1) (x - 1) = y$

Step 1

Rewrite the equation as $y = (x - 1) (x - 1) (x - 1)$ .

$y = (x - 1) (x - 1) (x - 1)$

Step 2

Simplify $(x - 1) (x - 1) (x - 1)$ .

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Step 2.1

Multiply $x - 1$ by $x - 1$ .

$y = {(x - 1)}^{2} (x - 1)$

Step 2.2

Multiply ${(x - 1)}^{2}$ by $x - 1$ by adding the exponents.

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Step 2.2.1

Multiply ${(x - 1)}^{2}$ by $x - 1$ .

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Step 2.2.1.1

Raise $x - 1$ to the power of $1$ .

$y = {(x - 1)}^{2} {(x - 1)}^{1}$

Step 2.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = {(x - 1)}^{2 + 1}$

Step 2.2.2

Add $2$ and $1$ .

$y = {(x - 1)}^{3}$

Step 2.3

Use the Binomial Theorem.

$y = x^{3} + 3 x^{2} \cdot - 1 + 3 x {(- 1)}^{2} + {(- 1)}^{3}$

Step 2.4

Simplify each term.

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Step 2.4.1

Multiply $- 1$ by $3$ .

$y = x^{3} - 3 x^{2} + 3 x {(- 1)}^{2} + {(- 1)}^{3}$

Step 2.4.2

Raise $- 1$ to the power of $2$ .

$y = x^{3} - 3 x^{2} + 3 x \cdot 1 + {(- 1)}^{3}$

Step 2.4.3

Multiply $3$ by $1$ .

$y = x^{3} - 3 x^{2} + 3 x + {(- 1)}^{3}$

Step 2.4.4

Raise $- 1$ to the power of $3$ .

$y = x^{3} - 3 x^{2} + 3 x - 1$