Basic Math Examples

$(12 z^{2} - \frac{6}{5} + \frac{4}{3} \cdot (z y)) - (3 z y + 2 y^{2})$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{4}{3} (z y)$ .

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Step 1.1.1

Combine $z$ and $\frac{4}{3}$ .

$12 z^{2} - \frac{6}{5} + \frac{z \cdot 4}{3} y - (3 z y + 2 y^{2})$

Step 1.1.2

Combine $\frac{z \cdot 4}{3}$ and $y$ .

$12 z^{2} - \frac{6}{5} + \frac{z \cdot 4 y}{3} - (3 z y + 2 y^{2})$

Step 1.2

Move $4$ to the left of $z$ .

$12 z^{2} - \frac{6}{5} + \frac{4 \cdot z y}{3} - (3 z y + 2 y^{2})$

Step 1.3

Apply the distributive property.

$12 z^{2} - \frac{6}{5} + \frac{4 z y}{3} - (3 z y) - (2 y^{2})$

Step 1.4

Multiply $3$ by $- 1$ .

$12 z^{2} - \frac{6}{5} + \frac{4 z y}{3} - 3 (z y) - (2 y^{2})$

Step 1.5

Multiply $2$ by $- 1$ .

$12 z^{2} - \frac{6}{5} + \frac{4 z y}{3} - 3 z y - 2 y^{2}$

Step 2

To write $- 3 z y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$12 z^{2} - \frac{6}{5} + \frac{4 z y}{3} - 3 z y \cdot \frac{3}{3} - 2 y^{2}$

Step 3

Simplify terms.

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Step 3.1

Combine $- 3 z y$ and $\frac{3}{3}$ .

$12 z^{2} - \frac{6}{5} + \frac{4 z y}{3} + \frac{- 3 z y \cdot 3}{3} - 2 y^{2}$

Step 3.2

Combine the numerators over the common denominator.

$12 z^{2} - \frac{6}{5} + \frac{4 z y - 3 z y \cdot 3}{3} - 2 y^{2}$

Step 4

Simplify each term.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Factor $z y$ out of $4 z y - 3 z y \cdot 3$ .

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Step 4.1.1.1

Factor $z y$ out of $4 z y$ .

$12 z^{2} - \frac{6}{5} + \frac{z y (4) - 3 z y \cdot 3}{3} - 2 y^{2}$

Step 4.1.1.2

Factor $z y$ out of $- 3 z y \cdot 3$ .

$12 z^{2} - \frac{6}{5} + \frac{z y (4) + z y (- 3 \cdot 3)}{3} - 2 y^{2}$

Step 4.1.1.3

Factor $z y$ out of $z y (4) + z y (- 3 \cdot 3)$ .

$12 z^{2} - \frac{6}{5} + \frac{z y (4 - 3 \cdot 3)}{3} - 2 y^{2}$

Step 4.1.2

Multiply $- 3$ by $3$ .

$12 z^{2} - \frac{6}{5} + \frac{z y (4 - 9)}{3} - 2 y^{2}$

Step 4.1.3

Subtract $9$ from $4$ .

$12 z^{2} - \frac{6}{5} + \frac{z y \cdot - 5}{3} - 2 y^{2}$

Step 4.2

Move $- 5$ to the left of $z y$ .

$12 z^{2} - \frac{6}{5} + \frac{- 5 \cdot (z y)}{3} - 2 y^{2}$

Step 4.3

Move the negative in front of the fraction.

$12 z^{2} - \frac{6}{5} - \frac{5 z y}{3} - 2 y^{2}$

Step 5

Simplify the expression.

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Step 5.1

Move $z$ .

$12 z^{2} - \frac{6}{5} - \frac{5 y z}{3} - 2 y^{2}$

Step 5.2

Move $- \frac{6}{5}$ .

$12 z^{2} - \frac{5 y z}{3} - 2 y^{2} - \frac{6}{5}$

Step 5.3

Move $12 z^{2}$ .

$- \frac{5 y z}{3} - 2 y^{2} + 12 z^{2} - \frac{6}{5}$

Step 5.4

Reorder $- \frac{5 y z}{3}$ and $- 2 y^{2}$ .

$- 2 y^{2} - \frac{5 y z}{3} + 12 z^{2} - \frac{6}{5}$