Algebra Examples

$(8 x^{2} - 3 x + \frac{1}{3}) - (2 x^{2} - 8 x + \frac{3}{5})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$8 x^{2} - 3 x + \frac{1}{3} - (2 x^{2}) - (- 8 x) - \frac{3}{5}$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $- 1$ .

$8 x^{2} - 3 x + \frac{1}{3} - 2 x^{2} - (- 8 x) - \frac{3}{5}$

Step 1.2.2

Multiply $- 8$ by $- 1$ .

$8 x^{2} - 3 x + \frac{1}{3} - 2 x^{2} + 8 x - \frac{3}{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x^{2}$ from $8 x^{2}$ .

$6 x^{2} - 3 x + \frac{1}{3} + 8 x - \frac{3}{5}$

Step 2.2

Add $- 3 x$ and $8 x$ .

$6 x^{2} + 5 x + \frac{1}{3} - \frac{3}{5}$

Step 3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$6 x^{2} + 5 x + \frac{1}{3} \cdot \frac{5}{5} - \frac{3}{5}$

Step 4

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$6 x^{2} + 5 x + \frac{1}{3} \cdot \frac{5}{5} - \frac{3}{5} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$6 x^{2} + 5 x + \frac{5}{3 \cdot 5} - \frac{3}{5} \cdot \frac{3}{3}$

Step 5.2

Multiply $3$ by $5$ .

$6 x^{2} + 5 x + \frac{5}{15} - \frac{3}{5} \cdot \frac{3}{3}$

Step 5.3

Multiply $\frac{3}{5}$ by $\frac{3}{3}$ .

$6 x^{2} + 5 x + \frac{5}{15} - \frac{3 \cdot 3}{5 \cdot 3}$

Step 5.4

Multiply $5$ by $3$ .

$6 x^{2} + 5 x + \frac{5}{15} - \frac{3 \cdot 3}{15}$

Step 6

Combine the numerators over the common denominator.

$6 x^{2} + 5 x + \frac{5 - 3 \cdot 3}{15}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 3$ by $3$ .

$6 x^{2} + 5 x + \frac{5 - 9}{15}$

Step 7.2

Subtract $9$ from $5$ .

$6 x^{2} + 5 x + \frac{- 4}{15}$

Step 8

Move the negative in front of the fraction.

$6 x^{2} + 5 x - \frac{4}{15}$