Pre-Algebra Examples

$10 x^{5} (5 x^{3} - 6 x^{2})$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$10 x^{5} (5 x^{3}) + 10 x^{5} (- 6 x^{2})$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$10 \cdot 5 x^{5} x^{3} + 10 x^{5} (- 6 x^{2})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$10 \cdot 5 x^{5} x^{3} + 10 \cdot - 6 x^{5} x^{2}$

Step 2

Simplify each term.

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Step 2.1

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

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Step 2.1.1

Move $x^{3}$ .

$10 \cdot 5 (x^{3} x^{5}) + 10 \cdot - 6 x^{5} x^{2}$

Step 2.1.2

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

$10 \cdot 5 x^{3 + 5} + 10 \cdot - 6 x^{5} x^{2}$

Step 2.1.3

Add $3$ and $5$ .

$10 \cdot 5 x^{8} + 10 \cdot - 6 x^{5} x^{2}$

Step 2.2

Multiply $10$ by $5$ .

$50 x^{8} + 10 \cdot - 6 x^{5} x^{2}$

Step 2.3

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

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Step 2.3.1

Move $x^{2}$ .

$50 x^{8} + 10 \cdot - 6 (x^{2} x^{5})$

Step 2.3.2

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

$50 x^{8} + 10 \cdot - 6 x^{2 + 5}$

Step 2.3.3

Add $2$ and $5$ .

$50 x^{8} + 10 \cdot - 6 x^{7}$

Step 2.4

Multiply $10$ by $- 6$ .

$50 x^{8} - 60 x^{7}$