Algebra Examples

$3 x^{3} \cdot 2 x^{2} y \cdot 4 x^{2} y$

Step 1

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

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Step 1.1

Move $x^{2}$ .

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

Step 1.2

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

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

Step 1.3

Add $2$ and $3$ .

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

Step 2

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

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Step 2.1

Move $x^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $2$ and $5$ .

$3 x^{7} \cdot (2 y) \cdot (4 y)$

Step 3

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

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Step 3.1

Move $y$ .

$3 x^{7} \cdot (2 (y \cdot y)) \cdot 4$

Step 3.2

Multiply $y$ by $y$ .

$3 x^{7} \cdot (2 y^{2}) \cdot 4$

Step 4

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x^{7} y^{2} \cdot 4$

Step 5

Multiply $3$ by $2$ .

$6 x^{7} y^{2} \cdot 4$

Step 6

Multiply $4$ by $6$ .

$24 x^{7} y^{2}$