Finite Math Examples

$(2 x + 9) (2 x + 9) = 4 x^{2} + 36 x + 81$

Step 1

Simplify $(2 x + 9) (2 x + 9)$ .

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Step 1.1

Rewrite.

$0 + 0 + (2 x + 9) (2 x + 9) = 4 x^{2} + 36 x + 81$

Step 1.2

Simplify by adding zeros.

$(2 x + 9) (2 x + 9) = 4 x^{2} + 36 x + 81$

Step 1.3

Expand $(2 x + 9) (2 x + 9)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$2 x (2 x + 9) + 9 (2 x + 9) = 4 x^{2} + 36 x + 81$

Step 1.3.2

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 9 + 9 (2 x + 9) = 4 x^{2} + 36 x + 81$

Step 1.3.3

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 9 + 9 (2 x) + 9 \cdot 9 = 4 x^{2} + 36 x + 81$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot 9 + 9 (2 x) + 9 \cdot 9 = 4 x^{2} + 36 x + 81$

Step 1.4.1.2

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

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Step 1.4.1.2.1

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot 9 + 9 (2 x) + 9 \cdot 9 = 4 x^{2} + 36 x + 81$

Step 1.4.1.2.2

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x \cdot 9 + 9 (2 x) + 9 \cdot 9 = 4 x^{2} + 36 x + 81$

Step 1.4.1.3

Multiply $2$ by $2$ .

$4 x^{2} + 2 x \cdot 9 + 9 (2 x) + 9 \cdot 9 = 4 x^{2} + 36 x + 81$

Step 1.4.1.4

Multiply $9$ by $2$ .

$4 x^{2} + 18 x + 9 (2 x) + 9 \cdot 9 = 4 x^{2} + 36 x + 81$

Step 1.4.1.5

Multiply $2$ by $9$ .

$4 x^{2} + 18 x + 18 x + 9 \cdot 9 = 4 x^{2} + 36 x + 81$

Step 1.4.1.6

Multiply $9$ by $9$ .

$4 x^{2} + 18 x + 18 x + 81 = 4 x^{2} + 36 x + 81$

Step 1.4.2

Add $18 x$ and $18 x$ .

$4 x^{2} + 36 x + 81 = 4 x^{2} + 36 x + 81$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $4 x^{2}$ from both sides of the equation.

$4 x^{2} + 36 x + 81 - 4 x^{2} = 36 x + 81$

Step 2.2

Subtract $36 x$ from both sides of the equation.

$4 x^{2} + 36 x + 81 - 4 x^{2} - 36 x = 81$

Step 2.3

Combine the opposite terms in $4 x^{2} + 36 x + 81 - 4 x^{2} - 36 x$ .

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Step 2.3.1

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

$36 x + 81 + 0 - 36 x = 81$

Step 2.3.2

Add $36 x + 81$ and $0$ .

$36 x + 81 - 36 x = 81$

Step 2.3.3

Subtract $36 x$ from $36 x$ .

$0 + 81 = 81$

Step 2.3.4

Add $0$ and $81$ .

$81 = 81$

Step 3

Since $81 = 81$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$