Simplify (2x^2+xy-y)(y^2+3x)

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

Step 1

Expand $(2 x^{2} + x y - y) (y^{2} + 3 x)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $3$ .

$2 x^{2} y^{2} + 6 x^{3} + x y \cdot y^{2} + x y (3 x) - y \cdot y^{2} - y (3 x)$

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

Move $y^{2}$ .

$2 x^{2} y^{2} + 6 x^{3} + x (y^{2} y) + x y (3 x) - y \cdot y^{2} - y (3 x)$

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

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

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

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

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

Add $2$ and $1$ .

$2 x^{2} y^{2} + 6 x^{3} + x y^{3} + x y (3 x) - y \cdot y^{2} - y (3 x)$

Rewrite using the commutative property of multiplication.

$2 x^{2} y^{2} + 6 x^{3} + x y^{3} + 3 x y x - y \cdot y^{2} - y (3 x)$

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

Move $x$ .

$2 x^{2} y^{2} + 6 x^{3} + x y^{3} + 3 (x \cdot x) y - y \cdot y^{2} - y (3 x)$

Multiply $x$ by $x$ .

$2 x^{2} y^{2} + 6 x^{3} + x y^{3} + 3 x^{2} y - y \cdot y^{2} - y (3 x)$

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

$2 x^{2} y^{2} + 6 x^{3} + x y^{3} + 3 x^{2} y - y^{3} - 1 \cdot 3 y x$

Multiply $- 1$ by $3$ .

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

Reorder.

Move $y$ .

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

Move $6 x^{3}$ .

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

Simplify (2x^2+xy-y)(y^2+3x)

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