Find the Product (x+2y)(x^2-xy+3y)

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

Step 1

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

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

Step 2

Simplify each term.

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

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

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

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $2$ by $3$ .

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

Step 3

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

Move $y$ .

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

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

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

Step 4

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

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

Find the Product (x+2y)(x^2-xy+3y)

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