Pre-Algebra Examples

$\frac{3 x^{4}}{7} - \frac{16 x^{2}}{21}$

Step 1

To write $\frac{3 x^{4}}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x^{4}}{7} \cdot \frac{3}{3} - \frac{16 x^{2}}{21}$

Step 2

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{3 x^{4}}{7}$ by $\frac{3}{3}$ .

$\frac{3 x^{4} \cdot 3}{7 \cdot 3} - \frac{16 x^{2}}{21}$

Step 2.2

Multiply $7$ by $3$ .

$\frac{3 x^{4} \cdot 3}{21} - \frac{16 x^{2}}{21}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 x^{4} \cdot 3 - 16 x^{2}}{21}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $x^{2}$ out of $3 x^{4} \cdot 3 - 16 x^{2}$ .

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Step 4.1.1

Factor $x^{2}$ out of $3 x^{4} \cdot 3$ .

$\frac{x^{2} (3 x^{2} \cdot 3) - 16 x^{2}}{21}$

Step 4.1.2

Factor $x^{2}$ out of $- 16 x^{2}$ .

$\frac{x^{2} (3 x^{2} \cdot 3) + x^{2} \cdot - 16}{21}$

Step 4.1.3

Factor $x^{2}$ out of $x^{2} (3 x^{2} \cdot 3) + x^{2} \cdot - 16$ .

$\frac{x^{2} (3 x^{2} \cdot 3 - 16)}{21}$

Step 4.2

Multiply $3$ by $3$ .

$\frac{x^{2} (9 x^{2} - 16)}{21}$

Step 4.3

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$\frac{x^{2} ({(3 x)}^{2} - 16)}{21}$

Step 4.4

Rewrite $16$ as $4^{2}$ .

$\frac{x^{2} ({(3 x)}^{2} - 4^{2})}{21}$

Step 4.5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = 4$ .

$\frac{x^{2} (3 x + 4) (3 x - 4)}{21}$