Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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.

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

Step 3.1.2

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

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Step 3.1.2.1

Move $x^{2}$ .

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

Step 3.1.2.2

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

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

Step 3.1.2.3

Add $2$ and $2$ .

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

Step 3.1.3

Multiply $- 9$ by $- 9$ .

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

Step 3.1.4

Rewrite using the commutative property of multiplication.

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

Step 3.1.5

Multiply $- 9$ by $- 10$ .

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

Step 3.1.6

Rewrite using the commutative property of multiplication.

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

Step 3.1.7

Multiply $- 10$ by $- 9$ .

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

Step 3.1.8

Rewrite using the commutative property of multiplication.

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

Step 3.1.9

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

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Step 3.1.9.1

Move $y$ .

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

Step 3.1.9.2

Multiply $y$ by $y$ .

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

Step 3.1.10

Multiply $- 10$ by $- 10$ .

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

Step 3.2

Add $90 x^{2} y$ and $90 y x^{2}$ .

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Step 3.2.1

Move $y$ .

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

Step 3.2.2

Add $90 x^{2} y$ and $90 x^{2} y$ .

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