Simplify (5x^4+y)^2

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

Step 1

Rewrite ${(5 x^{4} + y)}^{2}$ as $(5 x^{4} + y) (5 x^{4} + y)$ .

$(5 x^{4} + y) (5 x^{4} + y)$

Step 2

Expand $(5 x^{4} + y) (5 x^{4} + y)$ using the FOIL Method.

Apply the distributive property.

$5 x^{4} (5 x^{4} + y) + y (5 x^{4} + y)$

Apply the distributive property.

$5 x^{4} (5 x^{4}) + 5 x^{4} y + y (5 x^{4} + y)$

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{4}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

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

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

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

Add $4$ and $4$ .

$5 \cdot 5 x^{8} + 5 x^{4} y + y (5 x^{4}) + y \cdot y$

Multiply $5$ by $5$ .

$25 x^{8} + 5 x^{4} y + y (5 x^{4}) + y \cdot y$

Rewrite using the commutative property of multiplication.

$25 x^{8} + 5 x^{4} y + 5 y x^{4} + y \cdot y$

Multiply $y$ by $y$ .

$25 x^{8} + 5 x^{4} y + 5 y x^{4} + y^{2}$

Add $5 x^{4} y$ and $5 y x^{4}$ .

Move $y$ .

$25 x^{8} + 5 x^{4} y + 5 x^{4} y + y^{2}$

Add $5 x^{4} y$ and $5 x^{4} y$ .

$25 x^{8} + 10 x^{4} y + y^{2}$