Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

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

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Step 2.1

Move $x^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $2$ and $3$ .

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

Step 3

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1

Move $y$ .

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

Step 3.2

Multiply $y$ by $y$ .

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

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $4$ .

$12 x^{5} y + 4 x^{3} y^{2} \cdot - 5$

Step 4.2

Multiply $- 5$ by $4$ .

$12 x^{5} y - 20 x^{3} y^{2}$