Simplify (2x+y)(4x^2-2xy+y^2)

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

Expand $(2 x + y) (4 x^{2} - 2 x y + y^{2})$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $4$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 2$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

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

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

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

$8 x^{3} - 4 x^{2} y + 2 x y^{2} + 4 y x^{2} - 2 y^{2} x + y^{1} y^{2}$

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

$8 x^{3} - 4 x^{2} y + 2 x y^{2} + 4 y x^{2} - 2 y^{2} x + y^{1 + 2}$

Add $1$ and $2$ .

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

Combine the opposite terms in $8 x^{3} - 4 x^{2} y + 2 x y^{2} + 4 y x^{2} - 2 y^{2} x + y^{3}$ .

Reorder the factors in the terms $- 4 x^{2} y$ and $4 y x^{2}$ .

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

Add $- 4 x^{2} y$ and $4 x^{2} y$ .

$8 x^{3} + 2 x y^{2} + 0 - 2 y^{2} x + y^{3}$

Add $8 x^{3} + 2 x y^{2}$ and $0$ .

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

Reorder the factors in the terms $2 x y^{2}$ and $- 2 y^{2} x$ .

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

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

$8 x^{3} + 0 + y^{3}$

Add $8 x^{3}$ and $0$ .

$8 x^{3} + y^{3}$

Simplify (2x+y)(4x^2-2xy+y^2)

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