Basic Math Examples

$y (1 - y) (1 + y^{2}) - 2 y^{2} (2 y - 1)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $y$ by $1$ .

$(y + y (- y)) (1 + y^{2}) - 2 y^{2} (2 y - 1)$

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

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

Tap for more steps...

Step 1.4.1

Move $y$ .

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

Step 1.4.2

Multiply $y$ by $y$ .

$(y - y^{2}) (1 + y^{2}) - 2 y^{2} (2 y - 1)$

Step 1.5

Expand $(y - y^{2}) (1 + y^{2})$ using the FOIL Method.

Tap for more steps...

Step 1.5.1

Apply the distributive property.

$y (1 + y^{2}) - y^{2} (1 + y^{2}) - 2 y^{2} (2 y - 1)$

Step 1.5.2

Apply the distributive property.

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

Step 1.5.3

Apply the distributive property.

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

Step 1.6

Simplify each term.

Tap for more steps...

Step 1.6.1

Multiply $y$ by $1$ .

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

Step 1.6.2

Multiply $y$ by $y^{2}$ by adding the exponents.

Tap for more steps...

Step 1.6.2.1

Multiply $y$ by $y^{2}$ .

Tap for more steps...

Step 1.6.2.1.1

Raise $y$ to the power of $1$ .

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

Step 1.6.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.6.2.2

Add $1$ and $2$ .

$y + y^{3} - y^{2} \cdot 1 - y^{2} y^{2} - 2 y^{2} (2 y - 1)$

Step 1.6.3

Multiply $- 1$ by $1$ .

$y + y^{3} - y^{2} - y^{2} y^{2} - 2 y^{2} (2 y - 1)$

Step 1.6.4

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Tap for more steps...

Step 1.6.4.1

Move $y^{2}$ .

$y + y^{3} - y^{2} - (y^{2} y^{2}) - 2 y^{2} (2 y - 1)$

Step 1.6.4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y + y^{3} - y^{2} - y^{2 + 2} - 2 y^{2} (2 y - 1)$

Step 1.6.4.3

Add $2$ and $2$ .

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

Step 1.7

Apply the distributive property.

$y + y^{3} - y^{2} - y^{4} - 2 y^{2} (2 y) - 2 y^{2} \cdot - 1$

Step 1.8

Rewrite using the commutative property of multiplication.

$y + y^{3} - y^{2} - y^{4} - 2 \cdot 2 y^{2} y - 2 y^{2} \cdot - 1$

Step 1.9

Multiply $- 1$ by $- 2$ .

$y + y^{3} - y^{2} - y^{4} - 2 \cdot 2 y^{2} y + 2 y^{2}$

Step 1.10

Simplify each term.

Tap for more steps...

Step 1.10.1

Multiply $y^{2}$ by $y$ by adding the exponents.

Tap for more steps...

Step 1.10.1.1

Move $y$ .

$y + y^{3} - y^{2} - y^{4} - 2 \cdot 2 (y \cdot y^{2}) + 2 y^{2}$

Step 1.10.1.2

Multiply $y$ by $y^{2}$ .

Tap for more steps...

Step 1.10.1.2.1

Raise $y$ to the power of $1$ .

$y + y^{3} - y^{2} - y^{4} - 2 \cdot 2 (y^{1} y^{2}) + 2 y^{2}$

Step 1.10.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y + y^{3} - y^{2} - y^{4} - 2 \cdot 2 y^{1 + 2} + 2 y^{2}$

Step 1.10.1.3

Add $1$ and $2$ .

$y + y^{3} - y^{2} - y^{4} - 2 \cdot 2 y^{3} + 2 y^{2}$

Step 1.10.2

Multiply $- 2$ by $2$ .

$y + y^{3} - y^{2} - y^{4} - 4 y^{3} + 2 y^{2}$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Subtract $4 y^{3}$ from $y^{3}$ .

$y - 3 y^{3} - y^{2} - y^{4} + 2 y^{2}$

Step 2.2

Add $- y^{2}$ and $2 y^{2}$ .

$y - 3 y^{3} - y^{4} + y^{2}$

Step 2.3

Simplify the expression.

Tap for more steps...

Step 2.3.1

Move $y$ .

$- 3 y^{3} - y^{4} + y^{2} + y$

Step 2.3.2

Reorder $- 3 y^{3}$ and $- y^{4}$ .

$- y^{4} - 3 y^{3} + y^{2} + y$