Algebra Examples

$(2 x y) (- 4 x^{2}) + (6 x) (6 x^{2} y)$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Move $x^{2}$ .

$2 (x^{2} x) y \cdot - 4 + (6 x) (6 x^{2} y)$

Step 1.1.2

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

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Step 1.1.2.1

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

$2 (x^{2} x^{1}) y \cdot - 4 + (6 x) (6 x^{2} y)$

Step 1.1.2.2

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

$2 x^{2 + 1} y \cdot - 4 + (6 x) (6 x^{2} y)$

Step 1.1.3

Add $2$ and $1$ .

$2 x^{3} y \cdot - 4 + (6 x) (6 x^{2} y)$

Step 1.2

Multiply $- 4$ by $2$ .

$- 8 x^{3} y + (6 x) (6 x^{2} y)$

Step 1.3

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

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Step 1.3.1

Move $x^{2}$ .

$- 8 x^{3} y + 6 (x^{2} x) (6 y)$

Step 1.3.2

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

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Step 1.3.2.1

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

$- 8 x^{3} y + 6 (x^{2} x^{1}) (6 y)$

Step 1.3.2.2

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

$- 8 x^{3} y + 6 x^{2 + 1} (6 y)$

Step 1.3.3

Add $2$ and $1$ .

$- 8 x^{3} y + 6 x^{3} (6 y)$

Step 1.4

Rewrite using the commutative property of multiplication.

$- 8 x^{3} y + 6 \cdot 6 x^{3} y$

Step 1.5

Multiply $6$ by $6$ .

$- 8 x^{3} y + 36 x^{3} y$

Step 2

Add $- 8 x^{3} y$ and $36 x^{3} y$ .

$28 x^{3} y$