Algebra Examples

$(4 x^{2} y) (x^{3} - 3 x^{2} + 1)$

Step 1

Apply the distributive property.

$4 x^{2} y x^{3} + 4 x^{2} y (- 3 x^{2}) + 4 x^{2} y \cdot 1$

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x^{3}$ .

$4 (x^{3} x^{2}) y + 4 x^{2} y (- 3 x^{2}) + 4 x^{2} y \cdot 1$

Step 2.1.2

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

$4 x^{3 + 2} y + 4 x^{2} y (- 3 x^{2}) + 4 x^{2} y \cdot 1$

Step 2.1.3

Add $3$ and $2$ .

$4 x^{5} y + 4 x^{2} y (- 3 x^{2}) + 4 x^{2} y \cdot 1$

Step 2.2

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

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Step 2.2.1

Move $x^{2}$ .

$4 x^{5} y + 4 (x^{2} x^{2}) y \cdot - 3 + 4 x^{2} y \cdot 1$

Step 2.2.2

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

$4 x^{5} y + 4 x^{2 + 2} y \cdot - 3 + 4 x^{2} y \cdot 1$

Step 2.2.3

Add $2$ and $2$ .

$4 x^{5} y + 4 x^{4} y \cdot - 3 + 4 x^{2} y \cdot 1$

Step 2.3

Multiply $4$ by $1$ .

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

Step 3

Multiply $- 3$ by $4$ .

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