Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $4$ by $3$ .

$12 x^{2} + 3 x - (3 x^{2} + 3 x - 1)$

Step 1.3

Apply the distributive property.

$12 x^{2} + 3 x - (3 x^{2}) - (3 x) - - 1$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $3$ by $- 1$ .

$12 x^{2} + 3 x - 3 x^{2} - (3 x) - - 1$

Step 1.4.2

Multiply $3$ by $- 1$ .

$12 x^{2} + 3 x - 3 x^{2} - 3 x - - 1$

Step 1.4.3

Multiply $- 1$ by $- 1$ .

$12 x^{2} + 3 x - 3 x^{2} - 3 x + 1$

$12 x^{2} + 3 x - 3 x^{2} - 3 x + 1$

$12 x^{2} + 3 x - 3 x^{2} - 3 x + 1$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $12 x^{2} + 3 x - 3 x^{2} - 3 x + 1$ .

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Step 2.1.1

Subtract $3 x$ from $3 x$ .

$12 x^{2} - 3 x^{2} + 0 + 1$

Step 2.1.2

Add $12 x^{2} - 3 x^{2}$ and $0$ .

$12 x^{2} - 3 x^{2} + 1$

$12 x^{2} - 3 x^{2} + 1$

Step 2.2

Subtract $3 x^{2}$ from $12 x^{2}$ .

$9 x^{2} + 1$

$9 x^{2} + 1$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$