Precalculus Examples

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

Step 1

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

$(x - 9 y) (x - 9 y)$

Step 2

Expand $(x - 9 y) (x - 9 y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$x (x - 9 y) - 9 y (x - 9 y)$

Step 2.2

Apply the distributive property.

$x \cdot x + x (- 9 y) - 9 y (x - 9 y)$

Step 2.3

Apply the distributive property.

$x \cdot x + x (- 9 y) - 9 y x - 9 y (- 9 y)$

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

Multiply $x$ by $x$ .

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

Step 3.1.2

Rewrite using the commutative property of multiplication.

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

Step 3.1.3

Rewrite using the commutative property of multiplication.

$x^{2} - 9 x y - 9 y x - 9 \cdot - 9 y \cdot y$

Step 3.1.4

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

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Step 3.1.4.1

Move $y$ .

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

Step 3.1.4.2

Multiply $y$ by $y$ .

$x^{2} - 9 x y - 9 y x - 9 \cdot - 9 y^{2}$

Step 3.1.5

Multiply $- 9$ by $- 9$ .

$x^{2} - 9 x y - 9 y x + 81 y^{2}$

Step 3.2

Subtract $9 y x$ from $- 9 x y$ .

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Step 3.2.1

Move $y$ .

$x^{2} - 9 x y - 9 x y + 81 y^{2}$

Step 3.2.2

Subtract $9 x y$ from $- 9 x y$ .

$x^{2} - 18 x y + 81 y^{2}$