Algebra Examples

$(- 2 x^{3} y^{2} + 4 x^{2} y^{3} - 3 x y^{4}) - (6 x^{4} y - 5 x^{2} y^{3} - y^{5})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 2 x^{3} y^{2} + 4 x^{2} y^{3} - 3 x y^{4} - (6 x^{4} y) - (- 5 x^{2} y^{3}) - - y^{5}$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $6$ by $- 1$ .

$- 2 x^{3} y^{2} + 4 x^{2} y^{3} - 3 x y^{4} - 6 (x^{4} y) - (- 5 x^{2} y^{3}) - - y^{5}$

Step 1.2.2

Multiply $- 5$ by $- 1$ .

$- 2 x^{3} y^{2} + 4 x^{2} y^{3} - 3 x y^{4} - 6 (x^{4} y) + 5 (x^{2} y^{3}) - - y^{5}$

Step 1.2.3

Multiply $- - y^{5}$ .

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Step 1.2.3.1

Multiply $- 1$ by $- 1$ .

$- 2 x^{3} y^{2} + 4 x^{2} y^{3} - 3 x y^{4} - 6 (x^{4} y) + 5 (x^{2} y^{3}) + 1 y^{5}$

Step 1.2.3.2

Multiply $y^{5}$ by $1$ .

$- 2 x^{3} y^{2} + 4 x^{2} y^{3} - 3 x y^{4} - 6 (x^{4} y) + 5 (x^{2} y^{3}) + y^{5}$

Step 1.3

Remove parentheses.

$- 2 x^{3} y^{2} + 4 x^{2} y^{3} - 3 x y^{4} - 6 x^{4} y + 5 x^{2} y^{3} + y^{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $4 x^{2} y^{3}$ and $5 x^{2} y^{3}$ .

$- 2 x^{3} y^{2} + 9 x^{2} y^{3} - 3 x y^{4} - 6 x^{4} y + y^{5}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $- 3 x y^{4}$ .

$- 2 x^{3} y^{2} + 9 x^{2} y^{3} - 6 x^{4} y - 3 x y^{4} + y^{5}$

Step 2.2.2

Move $9 x^{2} y^{3}$ .

$- 2 x^{3} y^{2} - 6 x^{4} y + 9 x^{2} y^{3} - 3 x y^{4} + y^{5}$

Step 2.2.3

Reorder $- 2 x^{3} y^{2}$ and $- 6 x^{4} y$ .

$- 6 x^{4} y - 2 x^{3} y^{2} + 9 x^{2} y^{3} - 3 x y^{4} + y^{5}$