Algebra Examples

$5 x \cdot 2 y^{2} - 5 x \cdot 3 x y - x^{2} y + 6 x y^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 2 x y^{2} - 5 x \cdot (3 x y) - x^{2} y + 6 x y^{2}$

Step 1.2

Multiply $5$ by $2$ .

$10 x y^{2} - 5 x \cdot (3 x y) - x^{2} y + 6 x y^{2}$

Step 1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 1.3.1

Move $x$ .

$10 x y^{2} - 5 (x \cdot x) \cdot (3 y) - x^{2} y + 6 x y^{2}$

Step 1.3.2

Multiply $x$ by $x$ .

$10 x y^{2} - 5 x^{2} \cdot (3 y) - x^{2} y + 6 x y^{2}$

Step 1.4

Rewrite using the commutative property of multiplication.

$10 x y^{2} - 5 \cdot 3 x^{2} y - x^{2} y + 6 x y^{2}$

Step 1.5

Multiply $- 5$ by $3$ .

$10 x y^{2} - 15 x^{2} y - x^{2} y + 6 x y^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $10 x y^{2}$ and $6 x y^{2}$ .

$16 x y^{2} - 15 x^{2} y - x^{2} y$

Step 2.2

Subtract $x^{2} y$ from $- 15 x^{2} y$ .

$16 x y^{2} - 16 x^{2} y$