Algebra Examples

$x (2 x - 4) = (x - 2) (x - 2)$

Step 1

Subtract $(x - 2) (x - 2)$ from both sides of the equation.

$x (2 x - 4) - (x - 2) (x - 2) = 0$

Step 2

Simplify $x (2 x - 4) - (x - 2) (x - 2)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x (2 x) + x \cdot - 4 - (x - 2) (x - 2) = 0$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot - 4 - (x - 2) (x - 2) = 0$

Step 2.1.3

Move $- 4$ to the left of $x$ .

$2 x \cdot x - 4 \cdot x - (x - 2) (x - 2) = 0$

Step 2.1.4

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.4.1

Move $x$ .

$2 (x \cdot x) - 4 \cdot x - (x - 2) (x - 2) = 0$

Step 2.1.4.2

Multiply $x$ by $x$ .

$2 x^{2} - 4 \cdot x - (x - 2) (x - 2) = 0$

$2 x^{2} - 4 x - (x - 2) (x - 2) = 0$

Step 2.1.5

Apply the distributive property.

$2 x^{2} - 4 x + (- x - - 2) (x - 2) = 0$

Step 2.1.6

Multiply $- 1$ by $- 2$ .

$2 x^{2} - 4 x + (- x + 2) (x - 2) = 0$

Step 2.1.7

Expand $(- x + 2) (x - 2)$ using the FOIL Method.

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Step 2.1.7.1

Apply the distributive property.

$2 x^{2} - 4 x - x (x - 2) + 2 (x - 2) = 0$

Step 2.1.7.2

Apply the distributive property.

$2 x^{2} - 4 x - x \cdot x - x \cdot - 2 + 2 (x - 2) = 0$

Step 2.1.7.3

Apply the distributive property.

$2 x^{2} - 4 x - x \cdot x - x \cdot - 2 + 2 x + 2 \cdot - 2 = 0$

Step 2.1.8

Simplify and combine like terms.

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Step 2.1.8.1

Simplify each term.

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Step 2.1.8.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.8.1.1.1

Move $x$ .

$2 x^{2} - 4 x - (x \cdot x) - x \cdot - 2 + 2 x + 2 \cdot - 2 = 0$

Step 2.1.8.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} - 4 x - x^{2} - x \cdot - 2 + 2 x + 2 \cdot - 2 = 0$

Step 2.1.8.1.2

Multiply $- 2$ by $- 1$ .

$2 x^{2} - 4 x - x^{2} + 2 x + 2 x + 2 \cdot - 2 = 0$

Step 2.1.8.1.3

Multiply $2$ by $- 2$ .

$2 x^{2} - 4 x - x^{2} + 2 x + 2 x - 4 = 0$

Step 2.1.8.2

Add $2 x$ and $2 x$ .

$2 x^{2} - 4 x - x^{2} + 4 x - 4 = 0$

Step 2.2

Combine the opposite terms in $2 x^{2} - 4 x - x^{2} + 4 x - 4$ .

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Step 2.2.1

Add $- 4 x$ and $4 x$ .

$2 x^{2} - x^{2} + 0 - 4 = 0$

Step 2.2.2

Add $2 x^{2} - x^{2}$ and $0$ .

$2 x^{2} - x^{2} - 4 = 0$

Step 2.3

Subtract $x^{2}$ from $2 x^{2}$ .

$x^{2} - 4 = 0$

Step 3

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 4

The standard form is $x^{2} - 4$ .

$x^{2} - 4 = 0$

Step 5