Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

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

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Step 2.2.1

Move $x$ .

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

Step 2.2.2

Multiply $x$ by $x$ .

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

Step 2.3

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

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Step 2.3.1

Move $y$ .

$5 x^{2} y \cdot 2 + 5 x (y \cdot y) \cdot - 1 + 6 y^{2} (x^{2} + 6)$

Step 2.3.2

Multiply $y$ by $y$ .

$5 x^{2} y \cdot 2 + 5 x y^{2} \cdot - 1 + 6 y^{2} (x^{2} + 6)$

Step 2.4

Simplify each term.

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Step 2.4.1

Multiply $2$ by $5$ .

$10 x^{2} y + 5 x y^{2} \cdot - 1 + 6 y^{2} (x^{2} + 6)$

Step 2.4.2

Multiply $- 1$ by $5$ .

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

Step 2.5

Apply the distributive property.

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

Step 2.6

Multiply $6$ by $6$ .

$10 x^{2} y - 5 x y^{2} + 6 y^{2} x^{2} + 36 y^{2}$

Step 3

Simplify the expression.

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Step 3.1

Move $y^{2}$ .

$10 x^{2} y - 5 x y^{2} + 6 x^{2} y^{2} + 36 y^{2}$

Step 3.2

Move $- 5 x y^{2}$ .

$10 x^{2} y + 6 x^{2} y^{2} - 5 x y^{2} + 36 y^{2}$

Step 3.3

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

$6 x^{2} y^{2} + 10 x^{2} y - 5 x y^{2} + 36 y^{2}$