Calculus Examples

${(2 - y^{\frac{1}{3}})}^{2}$

Step 1

Rewrite ${(2 - y^{\frac{1}{3}})}^{2}$ as $(2 - y^{\frac{1}{3}}) (2 - y^{\frac{1}{3}})$ .

$(2 - y^{\frac{1}{3}}) (2 - y^{\frac{1}{3}})$

Step 2

Expand $(2 - y^{\frac{1}{3}}) (2 - y^{\frac{1}{3}})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 (2 - y^{\frac{1}{3}}) - y^{\frac{1}{3}} (2 - y^{\frac{1}{3}})$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2$ by $2$ .

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

Step 3.1.2

Multiply $- 1$ by $2$ .

$4 - 2 y^{\frac{1}{3}} - y^{\frac{1}{3}} \cdot 2 - y^{\frac{1}{3}} (- y^{\frac{1}{3}})$

Step 3.1.3

Multiply $2$ by $- 1$ .

$4 - 2 y^{\frac{1}{3}} - 2 y^{\frac{1}{3}} - y^{\frac{1}{3}} (- y^{\frac{1}{3}})$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$4 - 2 y^{\frac{1}{3}} - 2 y^{\frac{1}{3}} - 1 \cdot - 1 y^{\frac{1}{3}} y^{\frac{1}{3}}$

Step 3.1.5

Multiply $y^{\frac{1}{3}}$ by $y^{\frac{1}{3}}$ by adding the exponents.

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Step 3.1.5.1

Move $y^{\frac{1}{3}}$ .

$4 - 2 y^{\frac{1}{3}} - 2 y^{\frac{1}{3}} - 1 \cdot - 1 (y^{\frac{1}{3}} y^{\frac{1}{3}})$

Step 3.1.5.2

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

$4 - 2 y^{\frac{1}{3}} - 2 y^{\frac{1}{3}} - 1 \cdot - 1 y^{\frac{1}{3} + \frac{1}{3}}$

Step 3.1.5.3

Combine the numerators over the common denominator.

$4 - 2 y^{\frac{1}{3}} - 2 y^{\frac{1}{3}} - 1 \cdot - 1 y^{\frac{1 + 1}{3}}$

Step 3.1.5.4

Add $1$ and $1$ .

$4 - 2 y^{\frac{1}{3}} - 2 y^{\frac{1}{3}} - 1 \cdot - 1 y^{\frac{2}{3}}$

Step 3.1.6

Multiply $- 1$ by $- 1$ .

$4 - 2 y^{\frac{1}{3}} - 2 y^{\frac{1}{3}} + 1 y^{\frac{2}{3}}$

Step 3.1.7

Multiply $y^{\frac{2}{3}}$ by $1$ .

$4 - 2 y^{\frac{1}{3}} - 2 y^{\frac{1}{3}} + y^{\frac{2}{3}}$

Step 3.2

Subtract $2 y^{\frac{1}{3}}$ from $- 2 y^{\frac{1}{3}}$ .

$4 - 4 y^{\frac{1}{3}} + y^{\frac{2}{3}}$