Algebra Examples

${(6 y^{2} + 5 y^{4})}^{2}$

Step 1

Rewrite ${(6 y^{2} + 5 y^{4})}^{2}$ as $(6 y^{2} + 5 y^{4}) (6 y^{2} + 5 y^{4})$ .

$(6 y^{2} + 5 y^{4}) (6 y^{2} + 5 y^{4})$

Step 2

Expand $(6 y^{2} + 5 y^{4}) (6 y^{2} + 5 y^{4})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$6 y^{2} (6 y^{2} + 5 y^{4}) + 5 y^{4} (6 y^{2} + 5 y^{4})$

Step 2.2

Apply the distributive property.

$6 y^{2} (6 y^{2}) + 6 y^{2} (5 y^{4}) + 5 y^{4} (6 y^{2} + 5 y^{4})$

Step 2.3

Apply the distributive property.

$6 y^{2} (6 y^{2}) + 6 y^{2} (5 y^{4}) + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

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.

$6 \cdot 6 y^{2} y^{2} + 6 y^{2} (5 y^{4}) + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

Step 3.1.2

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

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Step 3.1.2.1

Move $y^{2}$ .

$6 \cdot 6 (y^{2} y^{2}) + 6 y^{2} (5 y^{4}) + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

Step 3.1.2.2

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

$6 \cdot 6 y^{2 + 2} + 6 y^{2} (5 y^{4}) + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

Step 3.1.2.3

Add $2$ and $2$ .

$6 \cdot 6 y^{4} + 6 y^{2} (5 y^{4}) + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

Step 3.1.3

Multiply $6$ by $6$ .

$36 y^{4} + 6 y^{2} (5 y^{4}) + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$36 y^{4} + 6 \cdot 5 y^{2} y^{4} + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

Step 3.1.5

Multiply $y^{2}$ by $y^{4}$ by adding the exponents.

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Step 3.1.5.1

Move $y^{4}$ .

$36 y^{4} + 6 \cdot 5 (y^{4} y^{2}) + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

Step 3.1.5.2

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

$36 y^{4} + 6 \cdot 5 y^{4 + 2} + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

Step 3.1.5.3

Add $4$ and $2$ .

$36 y^{4} + 6 \cdot 5 y^{6} + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

Step 3.1.6

Multiply $6$ by $5$ .

$36 y^{4} + 30 y^{6} + 5 y^{4} (6 y^{2}) + 5 y^{4} (5 y^{4})$

Step 3.1.7

Rewrite using the commutative property of multiplication.

$36 y^{4} + 30 y^{6} + 5 \cdot 6 y^{4} y^{2} + 5 y^{4} (5 y^{4})$

Step 3.1.8

Multiply $y^{4}$ by $y^{2}$ by adding the exponents.

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Step 3.1.8.1

Move $y^{2}$ .

$36 y^{4} + 30 y^{6} + 5 \cdot 6 (y^{2} y^{4}) + 5 y^{4} (5 y^{4})$

Step 3.1.8.2

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

$36 y^{4} + 30 y^{6} + 5 \cdot 6 y^{2 + 4} + 5 y^{4} (5 y^{4})$

Step 3.1.8.3

Add $2$ and $4$ .

$36 y^{4} + 30 y^{6} + 5 \cdot 6 y^{6} + 5 y^{4} (5 y^{4})$

Step 3.1.9

Multiply $5$ by $6$ .

$36 y^{4} + 30 y^{6} + 30 y^{6} + 5 y^{4} (5 y^{4})$

Step 3.1.10

Rewrite using the commutative property of multiplication.

$36 y^{4} + 30 y^{6} + 30 y^{6} + 5 \cdot 5 y^{4} y^{4}$

Step 3.1.11

Multiply $y^{4}$ by $y^{4}$ by adding the exponents.

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Step 3.1.11.1

Move $y^{4}$ .

$36 y^{4} + 30 y^{6} + 30 y^{6} + 5 \cdot 5 (y^{4} y^{4})$

Step 3.1.11.2

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

$36 y^{4} + 30 y^{6} + 30 y^{6} + 5 \cdot 5 y^{4 + 4}$

Step 3.1.11.3

Add $4$ and $4$ .

$36 y^{4} + 30 y^{6} + 30 y^{6} + 5 \cdot 5 y^{8}$

Step 3.1.12

Multiply $5$ by $5$ .

$36 y^{4} + 30 y^{6} + 30 y^{6} + 25 y^{8}$

Step 3.2

Add $30 y^{6}$ and $30 y^{6}$ .

$36 y^{4} + 60 y^{6} + 25 y^{8}$