Finite Math Examples

$x^{2} (4 x^{3} + 7 x - 5)$

Step 1

Apply the distributive property.

$x^{2} (4 x^{3}) + x^{2} (7 x) + x^{2} \cdot - 5$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$4 x^{2} x^{3} + x^{2} (7 x) + x^{2} \cdot - 5$

Step 2.2

Rewrite using the commutative property of multiplication.

$4 x^{2} x^{3} + 7 x^{2} x + x^{2} \cdot - 5$

Step 2.3

Move $- 5$ to the left of $x^{2}$ .

$4 x^{2} x^{3} + 7 x^{2} x - 5 \cdot x^{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 3.1.1

Move $x^{3}$ .

$4 (x^{3} x^{2}) + 7 x^{2} x - 5 \cdot x^{2}$

Step 3.1.2

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

$4 x^{3 + 2} + 7 x^{2} x - 5 \cdot x^{2}$

Step 3.1.3

Add $3$ and $2$ .

$4 x^{5} + 7 x^{2} x - 5 \cdot x^{2}$

Step 3.2

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

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Step 3.2.1

Move $x$ .

$4 x^{5} + 7 (x \cdot x^{2}) - 5 \cdot x^{2}$

Step 3.2.2

Multiply $x$ by $x^{2}$ .

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Step 3.2.2.1

Raise $x$ to the power of $1$ .

$4 x^{5} + 7 (x^{1} x^{2}) - 5 \cdot x^{2}$

Step 3.2.2.2

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

$4 x^{5} + 7 x^{1 + 2} - 5 \cdot x^{2}$

Step 3.2.3

Add $1$ and $2$ .

$4 x^{5} + 7 x^{3} - 5 \cdot x^{2}$

$4 x^{5} + 7 x^{3} - 5 x^{2}$