Basic Math Examples

${(- 9 y^{2} - 10 y)}^{2}$

Step 1

Rewrite ${(- 9 y^{2} - 10 y)}^{2}$ as $(- 9 y^{2} - 10 y) (- 9 y^{2} - 10 y)$ .

$(- 9 y^{2} - 10 y) (- 9 y^{2} - 10 y)$

Step 2

Expand $(- 9 y^{2} - 10 y) (- 9 y^{2} - 10 y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- 9 y^{2} (- 9 y^{2} - 10 y) - 10 y (- 9 y^{2} - 10 y)$

Step 2.2

Apply the distributive property.

$- 9 y^{2} (- 9 y^{2}) - 9 y^{2} (- 10 y) - 10 y (- 9 y^{2} - 10 y)$

Step 2.3

Apply the distributive property.

$- 9 y^{2} (- 9 y^{2}) - 9 y^{2} (- 10 y) - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

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.

$- 9 \cdot - 9 y^{2} y^{2} - 9 y^{2} (- 10 y) - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.2

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

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Step 3.1.2.1

Move $y^{2}$ .

$- 9 \cdot - 9 (y^{2} y^{2}) - 9 y^{2} (- 10 y) - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.2.2

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

$- 9 \cdot - 9 y^{2 + 2} - 9 y^{2} (- 10 y) - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.2.3

Add $2$ and $2$ .

$- 9 \cdot - 9 y^{4} - 9 y^{2} (- 10 y) - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.3

Multiply $- 9$ by $- 9$ .

$81 y^{4} - 9 y^{2} (- 10 y) - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$81 y^{4} - 9 \cdot - 10 y^{2} y - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.5

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

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Step 3.1.5.1

Move $y$ .

$81 y^{4} - 9 \cdot - 10 (y \cdot y^{2}) - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.5.2

Multiply $y$ by $y^{2}$ .

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Step 3.1.5.2.1

Raise $y$ to the power of $1$ .

$81 y^{4} - 9 \cdot - 10 (y^{1} y^{2}) - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.5.2.2

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

$81 y^{4} - 9 \cdot - 10 y^{1 + 2} - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.5.3

Add $1$ and $2$ .

$81 y^{4} - 9 \cdot - 10 y^{3} - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.6

Multiply $- 9$ by $- 10$ .

$81 y^{4} + 90 y^{3} - 10 y (- 9 y^{2}) - 10 y (- 10 y)$

Step 3.1.7

Rewrite using the commutative property of multiplication.

$81 y^{4} + 90 y^{3} - 10 \cdot - 9 y \cdot y^{2} - 10 y (- 10 y)$

Step 3.1.8

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

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Step 3.1.8.1

Move $y^{2}$ .

$81 y^{4} + 90 y^{3} - 10 \cdot - 9 (y^{2} y) - 10 y (- 10 y)$

Step 3.1.8.2

Multiply $y^{2}$ by $y$ .

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Step 3.1.8.2.1

Raise $y$ to the power of $1$ .

$81 y^{4} + 90 y^{3} - 10 \cdot - 9 (y^{2} y^{1}) - 10 y (- 10 y)$

Step 3.1.8.2.2

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

$81 y^{4} + 90 y^{3} - 10 \cdot - 9 y^{2 + 1} - 10 y (- 10 y)$

Step 3.1.8.3

Add $2$ and $1$ .

$81 y^{4} + 90 y^{3} - 10 \cdot - 9 y^{3} - 10 y (- 10 y)$

Step 3.1.9

Multiply $- 10$ by $- 9$ .

$81 y^{4} + 90 y^{3} + 90 y^{3} - 10 y (- 10 y)$

Step 3.1.10

Rewrite using the commutative property of multiplication.

$81 y^{4} + 90 y^{3} + 90 y^{3} - 10 \cdot - 10 y \cdot y$

Step 3.1.11

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1.11.1

Move $y$ .

$81 y^{4} + 90 y^{3} + 90 y^{3} - 10 \cdot - 10 (y \cdot y)$

Step 3.1.11.2

Multiply $y$ by $y$ .

$81 y^{4} + 90 y^{3} + 90 y^{3} - 10 \cdot - 10 y^{2}$

Step 3.1.12

Multiply $- 10$ by $- 10$ .

$81 y^{4} + 90 y^{3} + 90 y^{3} + 100 y^{2}$

Step 3.2

Add $90 y^{3}$ and $90 y^{3}$ .

$81 y^{4} + 180 y^{3} + 100 y^{2}$