Algebra Examples

$(y^{3} + 6 x^{2} y^{2} - 4 x y - 8) - (2 y^{3} - 7 x^{2} y^{2} - 2 x y - y + 8)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$y^{3} + 6 x^{2} y^{2} - 4 x y - 8 - (2 y^{3}) - (- 7 x^{2} y^{2}) - (- 2 x y) - - y - 1 \cdot 8$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $- 1$ .

$y^{3} + 6 x^{2} y^{2} - 4 x y - 8 - 2 y^{3} - (- 7 x^{2} y^{2}) - (- 2 x y) - - y - 1 \cdot 8$

Step 1.2.2

Multiply $- 7$ by $- 1$ .

$y^{3} + 6 x^{2} y^{2} - 4 x y - 8 - 2 y^{3} + 7 (x^{2} y^{2}) - (- 2 x y) - - y - 1 \cdot 8$

Step 1.2.3

Multiply $- 2$ by $- 1$ .

$y^{3} + 6 x^{2} y^{2} - 4 x y - 8 - 2 y^{3} + 7 (x^{2} y^{2}) + 2 (x y) - - y - 1 \cdot 8$

Step 1.2.4

Multiply $- - y$ .

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Step 1.2.4.1

Multiply $- 1$ by $- 1$ .

$y^{3} + 6 x^{2} y^{2} - 4 x y - 8 - 2 y^{3} + 7 (x^{2} y^{2}) + 2 (x y) + 1 y - 1 \cdot 8$

Step 1.2.4.2

Multiply $y$ by $1$ .

$y^{3} + 6 x^{2} y^{2} - 4 x y - 8 - 2 y^{3} + 7 (x^{2} y^{2}) + 2 (x y) + y - 1 \cdot 8$

Step 1.2.5

Multiply $- 1$ by $8$ .

$y^{3} + 6 x^{2} y^{2} - 4 x y - 8 - 2 y^{3} + 7 (x^{2} y^{2}) + 2 (x y) + y - 8$

Step 1.3

Remove parentheses.

$y^{3} + 6 x^{2} y^{2} - 4 x y - 8 - 2 y^{3} + 7 x^{2} y^{2} + 2 x y + y - 8$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 y^{3}$ from $y^{3}$ .

$- y^{3} + 6 x^{2} y^{2} - 4 x y - 8 + 7 x^{2} y^{2} + 2 x y + y - 8$

Step 2.2

Add $6 x^{2} y^{2}$ and $7 x^{2} y^{2}$ .

$- y^{3} + 13 x^{2} y^{2} - 4 x y - 8 + 2 x y + y - 8$

Step 2.3

Add $- 4 x y$ and $2 x y$ .

$- y^{3} + 13 x^{2} y^{2} - 2 x y - 8 + y - 8$

Step 2.4

Subtract $8$ from $- 8$ .

$- y^{3} + 13 x^{2} y^{2} - 2 x y + y - 16$