Finite Math Examples

$3 {(3 - 2 x)}^{2} + 2$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(3 - 2 x)}^{2}$ as $(3 - 2 x) (3 - 2 x)$ .

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

Step 1.2

Expand $(3 - 2 x) (3 - 2 x)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

$3 (3 \cdot 3 + 3 (- 2 x) - 2 x (3 - 2 x)) + 2$

Step 1.2.3

Apply the distributive property.

$3 (3 \cdot 3 + 3 (- 2 x) - 2 x \cdot 3 - 2 x (- 2 x)) + 2$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $3$ by $3$ .

$3 (9 + 3 (- 2 x) - 2 x \cdot 3 - 2 x (- 2 x)) + 2$

Step 1.3.1.2

Multiply $- 2$ by $3$ .

$3 (9 - 6 x - 2 x \cdot 3 - 2 x (- 2 x)) + 2$

Step 1.3.1.3

Multiply $3$ by $- 2$ .

$3 (9 - 6 x - 6 x - 2 x (- 2 x)) + 2$

Step 1.3.1.4

Rewrite using the commutative property of multiplication.

$3 (9 - 6 x - 6 x - 2 \cdot - 2 x \cdot x) + 2$

Step 1.3.1.5

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

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Step 1.3.1.5.1

Move $x$ .

$3 (9 - 6 x - 6 x - 2 \cdot - 2 (x \cdot x)) + 2$

Step 1.3.1.5.2

Multiply $x$ by $x$ .

$3 (9 - 6 x - 6 x - 2 \cdot - 2 x^{2}) + 2$

Step 1.3.1.6

Multiply $- 2$ by $- 2$ .

$3 (9 - 6 x - 6 x + 4 x^{2}) + 2$

Step 1.3.2

Subtract $6 x$ from $- 6 x$ .

$3 (9 - 12 x + 4 x^{2}) + 2$

Step 1.4

Apply the distributive property.

$3 \cdot 9 + 3 (- 12 x) + 3 (4 x^{2}) + 2$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $3$ by $9$ .

$27 + 3 (- 12 x) + 3 (4 x^{2}) + 2$

Step 1.5.2

Multiply $- 12$ by $3$ .

$27 - 36 x + 3 (4 x^{2}) + 2$

Step 1.5.3

Multiply $4$ by $3$ .

$27 - 36 x + 12 x^{2} + 2$

Step 2

Simplify the expression.

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Step 2.1

Add $27$ and $2$ .

$- 36 x + 12 x^{2} + 29$

Step 2.2

Reorder $- 36 x$ and $12 x^{2}$ .

$12 x^{2} - 36 x + 29$