Algebra Examples

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

Step 1

Use the Multinomial Theorem.

$x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} + 3 x^{2} \cdot - 1 + 6 x y \cdot - 1 + 3 y^{2} \cdot - 1 + 3 x {(- 1)}^{2} + 3 y {(- 1)}^{2} + {(- 1)}^{3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $- 1$ by $3$ .

$x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 3 x^{2} + 6 x y \cdot - 1 + 3 y^{2} \cdot - 1 + 3 x {(- 1)}^{2} + 3 y {(- 1)}^{2} + {(- 1)}^{3}$

Step 2.2

Multiply $- 1$ by $6$ .

$x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 3 x^{2} - 6 x y + 3 y^{2} \cdot - 1 + 3 x {(- 1)}^{2} + 3 y {(- 1)}^{2} + {(- 1)}^{3}$

Step 2.3

Multiply $- 1$ by $3$ .

$x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 3 x^{2} - 6 x y - 3 y^{2} + 3 x {(- 1)}^{2} + 3 y {(- 1)}^{2} + {(- 1)}^{3}$

Step 2.4

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

$x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 3 x^{2} - 6 x y - 3 y^{2} + 3 x \cdot 1 + 3 y {(- 1)}^{2} + {(- 1)}^{3}$

Step 2.5

Multiply $3$ by $1$ .

$x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 3 x^{2} - 6 x y - 3 y^{2} + 3 x + 3 y {(- 1)}^{2} + {(- 1)}^{3}$

Step 2.6

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

$x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 3 x^{2} - 6 x y - 3 y^{2} + 3 x + 3 y \cdot 1 + {(- 1)}^{3}$

Step 2.7

Multiply $3$ by $1$ .

$x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 3 x^{2} - 6 x y - 3 y^{2} + 3 x + 3 y + {(- 1)}^{3}$

Step 2.8

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

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