Trigonometry Examples

${(x - y)}^{4}$

Step 1

Use the Binomial Theorem.

$x^{4} + 4 x^{3} (- y) + 6 x^{2} {(- y)}^{2} + 4 x {(- y)}^{3} + {(- y)}^{4}$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$x^{4} + 4 \cdot - 1 x^{3} y + 6 x^{2} {(- y)}^{2} + 4 x {(- y)}^{3} + {(- y)}^{4}$

Step 2.2

Multiply $4$ by $- 1$ .

$x^{4} - 4 x^{3} y + 6 x^{2} {(- y)}^{2} + 4 x {(- y)}^{3} + {(- y)}^{4}$

Step 2.3

Apply the product rule to $- y$ .

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

Step 2.4

Rewrite using the commutative property of multiplication.

$x^{4} - 4 x^{3} y + 6 \cdot {(- 1)}^{2} x^{2} y^{2} + 4 x {(- y)}^{3} + {(- y)}^{4}$

Step 2.5

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

$x^{4} - 4 x^{3} y + 6 \cdot 1 x^{2} y^{2} + 4 x {(- y)}^{3} + {(- y)}^{4}$

Step 2.6

Multiply $6$ by $1$ .

$x^{4} - 4 x^{3} y + 6 x^{2} y^{2} + 4 x {(- y)}^{3} + {(- y)}^{4}$

Step 2.7

Apply the product rule to $- y$ .

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

Step 2.8

Rewrite using the commutative property of multiplication.

$x^{4} - 4 x^{3} y + 6 x^{2} y^{2} + 4 \cdot {(- 1)}^{3} x y^{3} + {(- y)}^{4}$

Step 2.9

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

$x^{4} - 4 x^{3} y + 6 x^{2} y^{2} + 4 \cdot - 1 x y^{3} + {(- y)}^{4}$

Step 2.10

Multiply $4$ by $- 1$ .

$x^{4} - 4 x^{3} y + 6 x^{2} y^{2} - 4 x y^{3} + {(- y)}^{4}$

Step 2.11

Apply the product rule to $- y$ .

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

Step 2.12

Raise $- 1$ to the power of $4$ .

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

Step 2.13

Multiply $y^{4}$ by $1$ .

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