Simplify (4x^3+y^4)^2

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

Step 1

Rewrite ${(4 x^{3} + y^{4})}^{2}$ as $(4 x^{3} + y^{4}) (4 x^{3} + y^{4})$ .

$(4 x^{3} + y^{4}) (4 x^{3} + y^{4})$

Step 2

Expand $(4 x^{3} + y^{4}) (4 x^{3} + y^{4})$ using the FOIL Method.

Apply the distributive property.

$4 x^{3} (4 x^{3} + y^{4}) + y^{4} (4 x^{3} + y^{4})$

Apply the distributive property.

$4 x^{3} (4 x^{3}) + 4 x^{3} y^{4} + y^{4} (4 x^{3} + y^{4})$

Apply the distributive property.

$4 x^{3} (4 x^{3}) + 4 x^{3} y^{4} + y^{4} (4 x^{3}) + y^{4} y^{4}$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

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

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

Add $3$ and $3$ .

$4 \cdot 4 x^{6} + 4 x^{3} y^{4} + y^{4} (4 x^{3}) + y^{4} y^{4}$

Multiply $4$ by $4$ .

$16 x^{6} + 4 x^{3} y^{4} + y^{4} (4 x^{3}) + y^{4} y^{4}$

Rewrite using the commutative property of multiplication.

$16 x^{6} + 4 x^{3} y^{4} + 4 y^{4} x^{3} + y^{4} y^{4}$

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

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

$16 x^{6} + 4 x^{3} y^{4} + 4 y^{4} x^{3} + y^{4 + 4}$

Add $4$ and $4$ .

$16 x^{6} + 4 x^{3} y^{4} + 4 y^{4} x^{3} + y^{8}$

Add $4 x^{3} y^{4}$ and $4 y^{4} x^{3}$ .

Move $y^{4}$ .

$16 x^{6} + 4 x^{3} y^{4} + 4 x^{3} y^{4} + y^{8}$

Add $4 x^{3} y^{4}$ and $4 x^{3} y^{4}$ .

$16 x^{6} + 8 x^{3} y^{4} + y^{8}$

Step 4

Move $16 x^{6}$ .

$8 x^{3} y^{4} + y^{8} + 16 x^{6}$

Step 5

Reorder $8 x^{3} y^{4}$ and $y^{8}$ .

$y^{8} + 8 x^{3} y^{4} + 16 x^{6}$