Algebra Examples

{(2 x - 1)}^{2}

${(2 x - 1)}^{2}$

Step 1

Rewrite

${(2 x - 1)}^{2}$ as

$(2 x - 1) (2 x - 1)$ .

$(2 x - 1) (2 x - 1)$

Step 2

Expand

$(2 x - 1) (2 x - 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 x (2 x - 1) - 1 (2 x - 1)$

Step 2.2

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 1 - 1 (2 x - 1)$

Step 2.3

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 1 - 1 (2 x) - 1 \cdot - 1$

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.

$2 \cdot 2 x \cdot x + 2 x \cdot - 1 - 1 (2 x) - 1 \cdot - 1$

Step 3.1.2

Multiply

$x$ by

$x$ by adding the exponents.

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Step 3.1.2.1

Move

$x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot - 1 - 1 (2 x) - 1 \cdot - 1$

Step 3.1.2.2

Multiply

$x$ by

$x$ .

$2 \cdot 2 x^{2} + 2 x \cdot - 1 - 1 (2 x) - 1 \cdot - 1$

Step 3.1.3

Multiply

$2$ by

$2$ .

$4 x^{2} + 2 x \cdot - 1 - 1 (2 x) - 1 \cdot - 1$

Step 3.1.4

Multiply

$- 1$ by

$2$ .

$4 x^{2} - 2 x - 1 (2 x) - 1 \cdot - 1$

Step 3.1.5

Multiply

$2$ by

$- 1$ .

$4 x^{2} - 2 x - 2 x - 1 \cdot - 1$

Step 3.1.6

Multiply

$- 1$ by

$- 1$ .

$4 x^{2} - 2 x - 2 x + 1$

Step 3.2

Subtract

$2 x$ from

$- 2 x$ .

$4 x^{2} - 4 x + 1$

${(2 x - 1)}^{2}$

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