Basic Math Examples

$(4 a^{2} - 2 a^{5}) \cdot (10 a^{4})$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$4 a^{2} (10 a^{4}) - 2 a^{5} (10 a^{4})$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$4 \cdot 10 a^{2} a^{4} - 2 a^{5} (10 a^{4})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$4 \cdot 10 a^{2} a^{4} - 2 \cdot 10 a^{5} a^{4}$

Step 2

Simplify each term.

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Step 2.1

Multiply $a^{2}$ by $a^{4}$ by adding the exponents.

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Step 2.1.1

Move $a^{4}$ .

$4 \cdot 10 (a^{4} a^{2}) - 2 \cdot 10 a^{5} a^{4}$

Step 2.1.2

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

$4 \cdot 10 a^{4 + 2} - 2 \cdot 10 a^{5} a^{4}$

Step 2.1.3

Add $4$ and $2$ .

$4 \cdot 10 a^{6} - 2 \cdot 10 a^{5} a^{4}$

Step 2.2

Multiply $4$ by $10$ .

$40 a^{6} - 2 \cdot 10 a^{5} a^{4}$

Step 2.3

Multiply $a^{5}$ by $a^{4}$ by adding the exponents.

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Step 2.3.1

Move $a^{4}$ .

$40 a^{6} - 2 \cdot 10 (a^{4} a^{5})$

Step 2.3.2

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

$40 a^{6} - 2 \cdot 10 a^{4 + 5}$

Step 2.3.3

Add $4$ and $5$ .

$40 a^{6} - 2 \cdot 10 a^{9}$

Step 2.4

Multiply $- 2$ by $10$ .

$40 a^{6} - 20 a^{9}$