Basic Math Examples

${(3 z + y^{5})}^{2}$

Step 1

Rewrite ${(3 z + y^{5})}^{2}$ as $(3 z + y^{5}) (3 z + y^{5})$ .

$(3 z + y^{5}) (3 z + y^{5})$

Step 2

Expand $(3 z + y^{5}) (3 z + y^{5})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$3 z (3 z + y^{5}) + y^{5} (3 z + y^{5})$

Step 2.2

Apply the distributive property.

$3 z (3 z) + 3 z y^{5} + y^{5} (3 z + y^{5})$

Step 2.3

Apply the distributive property.

$3 z (3 z) + 3 z y^{5} + y^{5} (3 z) + y^{5} y^{5}$

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

Rewrite using the commutative property of multiplication.

$3 \cdot 3 z \cdot z + 3 z y^{5} + y^{5} (3 z) + y^{5} y^{5}$

Step 3.1.2

Multiply $z$ by $z$ by adding the exponents.

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Step 3.1.2.1

Move $z$ .

$3 \cdot 3 (z \cdot z) + 3 z y^{5} + y^{5} (3 z) + y^{5} y^{5}$

Step 3.1.2.2

Multiply $z$ by $z$ .

$3 \cdot 3 z^{2} + 3 z y^{5} + y^{5} (3 z) + y^{5} y^{5}$

Step 3.1.3

Multiply $3$ by $3$ .

$9 z^{2} + 3 z y^{5} + y^{5} (3 z) + y^{5} y^{5}$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$9 z^{2} + 3 z y^{5} + 3 y^{5} z + y^{5} y^{5}$

Step 3.1.5

Multiply $y^{5}$ by $y^{5}$ by adding the exponents.

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Step 3.1.5.1

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

$9 z^{2} + 3 z y^{5} + 3 y^{5} z + y^{5 + 5}$

Step 3.1.5.2

Add $5$ and $5$ .

$9 z^{2} + 3 z y^{5} + 3 y^{5} z + y^{10}$

Step 3.2

Add $3 z y^{5}$ and $3 y^{5} z$ .

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Step 3.2.1

Move $z$ .

$9 z^{2} + 3 y^{5} z + 3 y^{5} z + y^{10}$

Step 3.2.2

Add $3 y^{5} z$ and $3 y^{5} z$ .

$9 z^{2} + 6 y^{5} z + y^{10}$

Step 4

Move $9 z^{2}$ .

$6 y^{5} z + y^{10} + 9 z^{2}$

Step 5

Reorder $6 y^{5} z$ and $y^{10}$ .

$y^{10} + 6 y^{5} z + 9 z^{2}$