Simplify (4x^5+y^3)^2

${(4 x^{5} + y^{3})}^{2}$

Step 1

Rewrite ${(4 x^{5} + y^{3})}^{2}$ as $(4 x^{5} + y^{3}) (4 x^{5} + y^{3})$ .

$(4 x^{5} + y^{3}) (4 x^{5} + y^{3})$

Step 2

Expand $(4 x^{5} + y^{3}) (4 x^{5} + y^{3})$ using the FOIL Method.

Apply the distributive property.

$4 x^{5} (4 x^{5} + y^{3}) + y^{3} (4 x^{5} + y^{3})$

Apply the distributive property.

$4 x^{5} (4 x^{5}) + 4 x^{5} y^{3} + y^{3} (4 x^{5} + y^{3})$

Apply the distributive property.

$4 x^{5} (4 x^{5}) + 4 x^{5} y^{3} + y^{3} (4 x^{5}) + y^{3} y^{3}$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x^{5} x^{5} + 4 x^{5} y^{3} + y^{3} (4 x^{5}) + y^{3} y^{3}$

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

Move $x^{5}$ .

$4 \cdot 4 (x^{5} x^{5}) + 4 x^{5} y^{3} + y^{3} (4 x^{5}) + y^{3} y^{3}$

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

$4 \cdot 4 x^{5 + 5} + 4 x^{5} y^{3} + y^{3} (4 x^{5}) + y^{3} y^{3}$

Add $5$ and $5$ .

$4 \cdot 4 x^{10} + 4 x^{5} y^{3} + y^{3} (4 x^{5}) + y^{3} y^{3}$

Multiply $4$ by $4$ .

$16 x^{10} + 4 x^{5} y^{3} + y^{3} (4 x^{5}) + y^{3} y^{3}$

Rewrite using the commutative property of multiplication.

$16 x^{10} + 4 x^{5} y^{3} + 4 y^{3} x^{5} + y^{3} y^{3}$

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

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

$16 x^{10} + 4 x^{5} y^{3} + 4 y^{3} x^{5} + y^{3 + 3}$

Add $3$ and $3$ .

$16 x^{10} + 4 x^{5} y^{3} + 4 y^{3} x^{5} + y^{6}$

Add $4 x^{5} y^{3}$ and $4 y^{3} x^{5}$ .

Move $y^{3}$ .

$16 x^{10} + 4 x^{5} y^{3} + 4 x^{5} y^{3} + y^{6}$

Add $4 x^{5} y^{3}$ and $4 x^{5} y^{3}$ .

$16 x^{10} + 8 x^{5} y^{3} + y^{6}$