Algebra Examples

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

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify the expression.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.2.2

Multiply $5$ by $- 2$ .

$- 2 \cdot - 3 x^{2} x^{\frac{1}{2}} - 10 x^{2}$

Step 2

Simplify each term.

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Step 2.1

Multiply $x^{2}$ by $x^{\frac{1}{2}}$ by adding the exponents.

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Step 2.1.1

Move $x^{\frac{1}{2}}$ .

$- 2 \cdot - 3 (x^{\frac{1}{2}} x^{2}) - 10 x^{2}$

Step 2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 \cdot - 3 x^{\frac{1}{2} + 2} - 10 x^{2}$

Step 2.1.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 \cdot - 3 x^{\frac{1}{2} + 2 \cdot \frac{2}{2}} - 10 x^{2}$

Step 2.1.4

Combine $2$ and $\frac{2}{2}$ .

$- 2 \cdot - 3 x^{\frac{1}{2} + \frac{2 \cdot 2}{2}} - 10 x^{2}$

Step 2.1.5

Combine the numerators over the common denominator.

$- 2 \cdot - 3 x^{\frac{1 + 2 \cdot 2}{2}} - 10 x^{2}$

Step 2.1.6

Simplify the numerator.

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Step 2.1.6.1

Multiply $2$ by $2$ .

$- 2 \cdot - 3 x^{\frac{1 + 4}{2}} - 10 x^{2}$

Step 2.1.6.2

Add $1$ and $4$ .

$- 2 \cdot - 3 x^{\frac{5}{2}} - 10 x^{2}$

Step 2.2

Multiply $- 2$ by $- 3$ .

$6 x^{\frac{5}{2}} - 10 x^{2}$