Algebra Examples

$(2 x - 1) (2 x + 1) = x (2 x + 3)$

Step 1

Subtract $x (2 x + 3)$ from both sides of the equation.

$(2 x - 1) (2 x + 1) - x (2 x + 3) = 0$

Step 2

Simplify $(2 x - 1) (2 x + 1) - x (2 x + 3)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

$2 x (2 x + 1) - 1 (2 x + 1) - x (2 x + 3) = 0$

Step 2.1.1.2

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 1 - 1 (2 x + 1) - x (2 x + 3) = 0$

Step 2.1.1.3

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 1 - 1 (2 x) - 1 \cdot 1 - x (2 x + 3) = 0$

Step 2.1.2

Combine the opposite terms in $2 x (2 x) + 2 x \cdot 1 - 1 (2 x) - 1 \cdot 1$ .

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Step 2.1.2.1

Reorder the factors in the terms $2 x \cdot 1$ and $- 1 (2 x)$ .

$2 x (2 x) + 1 \cdot 2 x - 1 \cdot 2 x - 1 \cdot 1 - x (2 x + 3) = 0$

Step 2.1.2.2

Subtract $2 x$ from $1 \cdot 2 x$ .

$2 x (2 x) + 0 - 1 \cdot 1 - x (2 x + 3) = 0$

Step 2.1.2.3

Add $2 x (2 x)$ and $0$ .

$2 x (2 x) - 1 \cdot 1 - x (2 x + 3) = 0$

Step 2.1.3

Simplify each term.

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Step 2.1.3.1

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x - 1 \cdot 1 - x (2 x + 3) = 0$

Step 2.1.3.2

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

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Step 2.1.3.2.1

Move $x$ .

$2 \cdot 2 (x \cdot x) - 1 \cdot 1 - x (2 x + 3) = 0$

Step 2.1.3.2.2

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} - 1 \cdot 1 - x (2 x + 3) = 0$

Step 2.1.3.3

Multiply $2$ by $2$ .

$4 x^{2} - 1 \cdot 1 - x (2 x + 3) = 0$

Step 2.1.3.4

Multiply $- 1$ by $1$ .

$4 x^{2} - 1 - x (2 x + 3) = 0$

Step 2.1.4

Apply the distributive property.

$4 x^{2} - 1 - x (2 x) - x \cdot 3 = 0$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$4 x^{2} - 1 - 1 \cdot 2 x \cdot x - x \cdot 3 = 0$

Step 2.1.6

Multiply $3$ by $- 1$ .

$4 x^{2} - 1 - 1 \cdot 2 x \cdot x - 3 x = 0$

Step 2.1.7

Simplify each term.

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Step 2.1.7.1

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

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Step 2.1.7.1.1

Move $x$ .

$4 x^{2} - 1 - 1 \cdot 2 (x \cdot x) - 3 x = 0$

Step 2.1.7.1.2

Multiply $x$ by $x$ .

$4 x^{2} - 1 - 1 \cdot 2 x^{2} - 3 x = 0$

Step 2.1.7.2

Multiply $- 1$ by $2$ .

$4 x^{2} - 1 - 2 x^{2} - 3 x = 0$

Step 2.2

Subtract $2 x^{2}$ from $4 x^{2}$ .

$2 x^{2} - 1 - 3 x = 0$

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

Move $- 1$ .

$2 x^{2} - 3 x - 1 = 0$

Step 5