Pre-Algebra Examples

${(2 x - 5 y)}^{2}$

Step 1

Rewrite

${(2 x - 5 y)}^{2}$ as

$(2 x - 5 y) (2 x - 5 y)$ .

$(2 x - 5 y) (2 x - 5 y)$

Step 2

Expand

$(2 x - 5 y) (2 x - 5 y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 x (2 x - 5 y) - 5 y (2 x - 5 y)$

Step 2.2

Apply the distributive property.

$2 x (2 x) + 2 x (- 5 y) - 5 y (2 x - 5 y)$

Step 2.3

Apply the distributive property.

$2 x (2 x) + 2 x (- 5 y) - 5 y (2 x) - 5 y (- 5 y)$

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.

$2 \cdot 2 x \cdot x + 2 x (- 5 y) - 5 y (2 x) - 5 y (- 5 y)$

Step 3.1.2

Multiply

$x$ by

$x$ by adding the exponents.

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Step 3.1.2.1

Move

$x$ .

$2 \cdot 2 (x \cdot x) + 2 x (- 5 y) - 5 y (2 x) - 5 y (- 5 y)$

Step 3.1.2.2

Multiply

$x$ by

$x$ .

$2 \cdot 2 x^{2} + 2 x (- 5 y) - 5 y (2 x) - 5 y (- 5 y)$

Step 3.1.3

Multiply

$2$ by

$2$ .

$4 x^{2} + 2 x (- 5 y) - 5 y (2 x) - 5 y (- 5 y)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

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

Step 3.1.5

Multiply

$2$ by

$- 5$ .

$4 x^{2} - 10 x y - 5 y (2 x) - 5 y (- 5 y)$

Step 3.1.6

Rewrite using the commutative property of multiplication.

$4 x^{2} - 10 x y - 5 \cdot 2 y x - 5 y (- 5 y)$

Step 3.1.7

Multiply

$- 5$ by

$2$ .

$4 x^{2} - 10 x y - 10 y x - 5 y (- 5 y)$

Step 3.1.8

Rewrite using the commutative property of multiplication.

$4 x^{2} - 10 x y - 10 y x - 5 \cdot - 5 y \cdot y$

Step 3.1.9

Multiply

$y$ by

$y$ by adding the exponents.

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Step 3.1.9.1

Move

$y$ .

$4 x^{2} - 10 x y - 10 y x - 5 \cdot - 5 (y \cdot y)$

Step 3.1.9.2

Multiply

$y$ by

$y$ .

$4 x^{2} - 10 x y - 10 y x - 5 \cdot - 5 y^{2}$

Step 3.1.10

Multiply

$- 5$ by

$- 5$ .

$4 x^{2} - 10 x y - 10 y x + 25 y^{2}$

Step 3.2

Subtract

$10 y x$ from

$- 10 x y$ .

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Step 3.2.1

Move

$y$ .

$4 x^{2} - 10 x y - 10 x y + 25 y^{2}$

Step 3.2.2

Subtract

$10 x y$ from

$- 10 x y$ .

$4 x^{2} - 20 x y + 25 y^{2}$