Algebra Examples

$(2 a y^{2} + 5 y^{3}) - (- 8 a^{3} - 11 a^{2} y) + (- 10 a^{2} y - a y^{2})$

Step 1

Remove parentheses.

$(2 a y^{2} + 5 y^{3}) - (- 8 a^{3} - 11 a^{2} y) - 10 a^{2} y - a y^{2}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$2 a y^{2} + 5 y^{3} - (- 8 a^{3}) - (- 11 a^{2} y) - 10 a^{2} y - a y^{2}$

Step 2.2

Multiply $- 8$ by $- 1$ .

$2 a y^{2} + 5 y^{3} + 8 a^{3} - (- 11 a^{2} y) - 10 a^{2} y - a y^{2}$

Step 2.3

Multiply $- 11$ by $- 1$ .

$2 a y^{2} + 5 y^{3} + 8 a^{3} + 11 a^{2} y - 10 a^{2} y - a y^{2}$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $a y^{2}$ from $2 a y^{2}$ .

$5 y^{3} + 8 a^{3} + 11 a^{2} y - 10 a^{2} y + 1 a y^{2}$

Step 3.2

Multiply $a$ by $1$ .

$5 y^{3} + 8 a^{3} + 11 a^{2} y - 10 a^{2} y + a y^{2}$

Step 3.3

Subtract $10 a^{2} y$ from $11 a^{2} y$ .

$5 y^{3} + 8 a^{3} + 1 a^{2} y + a y^{2}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Multiply $a^{2}$ by $1$ .

$5 y^{3} + 8 a^{3} + a^{2} y + a y^{2}$

Step 3.4.2

Move $5 y^{3}$ .

$8 a^{3} + a^{2} y + a y^{2} + 5 y^{3}$