Simplify (2x^5+y)^2

${(2 x^{5} + y)}^{2}$

Step 1

Rewrite ${(2 x^{5} + y)}^{2}$ as $(2 x^{5} + y) (2 x^{5} + y)$ .

$(2 x^{5} + y) (2 x^{5} + y)$

Step 2

Expand $(2 x^{5} + y) (2 x^{5} + y)$ using the FOIL Method.

Apply the distributive property.

$2 x^{5} (2 x^{5} + y) + y (2 x^{5} + y)$

Apply the distributive property.

$2 x^{5} (2 x^{5}) + 2 x^{5} y + y (2 x^{5} + y)$

Apply the distributive property.

$2 x^{5} (2 x^{5}) + 2 x^{5} y + y (2 x^{5}) + y \cdot y$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x^{5} x^{5} + 2 x^{5} y + y (2 x^{5}) + y \cdot y$

Multiply $x^{5}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$2 \cdot 2 (x^{5} x^{5}) + 2 x^{5} y + y (2 x^{5}) + y \cdot y$

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

$2 \cdot 2 x^{5 + 5} + 2 x^{5} y + y (2 x^{5}) + y \cdot y$

Add $5$ and $5$ .

$2 \cdot 2 x^{10} + 2 x^{5} y + y (2 x^{5}) + y \cdot y$

Multiply $2$ by $2$ .

$4 x^{10} + 2 x^{5} y + y (2 x^{5}) + y \cdot y$

Rewrite using the commutative property of multiplication.

$4 x^{10} + 2 x^{5} y + 2 y x^{5} + y \cdot y$

Multiply $y$ by $y$ .

$4 x^{10} + 2 x^{5} y + 2 y x^{5} + y^{2}$

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

Move $y$ .

$4 x^{10} + 2 x^{5} y + 2 x^{5} y + y^{2}$

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

$4 x^{10} + 4 x^{5} y + y^{2}$