Algebra Examples

$(5 x - 4 y) (5 x + 4 y)$

Step 1

Expand

$(5 x - 4 y) (5 x + 4 y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$5 x (5 x + 4 y) - 4 y (5 x + 4 y)$

Step 1.2

Apply the distributive property.

$5 x (5 x) + 5 x (4 y) - 4 y (5 x + 4 y)$

Step 1.3

Apply the distributive property.

$5 x (5 x) + 5 x (4 y) - 4 y (5 x) - 4 y (4 y)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

$5 x (5 x) + 5 x (4 y) - 4 y (5 x) - 4 y (4 y)$ .

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Step 2.1.1

Reorder the factors in the terms

$5 x (4 y)$ and

$- 4 y (5 x)$ .

$5 x (5 x) + 4 \cdot 5 x y - 4 \cdot 5 x y - 4 y (4 y)$

Step 2.1.2

Subtract

$4 \cdot 5 x y$ from

$4 \cdot 5 x y$ .

$5 x (5 x) + 0 - 4 y (4 y)$

Step 2.1.3

Add

$5 x (5 x)$ and

$0$ .

$5 x (5 x) - 4 y (4 y)$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x - 4 y (4 y)$

Step 2.2.2

Multiply

$x$ by

$x$ by adding the exponents.

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Step 2.2.2.1

Move

$x$ .

$5 \cdot 5 (x \cdot x) - 4 y (4 y)$

Step 2.2.2.2

Multiply

$x$ by

$x$ .

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

Step 2.2.3

Multiply

$5$ by

$5$ .

$25 x^{2} - 4 y (4 y)$

Step 2.2.4

Rewrite using the commutative property of multiplication.

$25 x^{2} - 4 \cdot 4 y \cdot y$

Step 2.2.5

Multiply

$y$ by

$y$ by adding the exponents.

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Step 2.2.5.1

Move

$y$ .

$25 x^{2} - 4 \cdot 4 (y \cdot y)$

Step 2.2.5.2

Multiply

$y$ by

$y$ .

$25 x^{2} - 4 \cdot 4 y^{2}$

Step 2.2.6

Multiply

$- 4$ by

$4$ .

$25 x^{2} - 16 y^{2}$

$(5 x - 4 y) (5 x + 4 y)$

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