Simplify (x^3+x^6)^2

${(x^{3} + x^{6})}^{2}$

Step 1

Rewrite ${(x^{3} + x^{6})}^{2}$ as $(x^{3} + x^{6}) (x^{3} + x^{6})$ .

$(x^{3} + x^{6}) (x^{3} + x^{6})$

Step 2

Expand $(x^{3} + x^{6}) (x^{3} + x^{6})$ using the FOIL Method.

Apply the distributive property.

$x^{3} (x^{3} + x^{6}) + x^{6} (x^{3} + x^{6})$

Apply the distributive property.

$x^{3} x^{3} + x^{3} x^{6} + x^{6} (x^{3} + x^{6})$

Apply the distributive property.

$x^{3} x^{3} + x^{3} x^{6} + x^{6} x^{3} + x^{6} x^{6}$

Step 3

Simplify and combine like terms.

Simplify each term.

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

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

$x^{3 + 3} + x^{3} x^{6} + x^{6} x^{3} + x^{6} x^{6}$

Add $3$ and $3$ .

$x^{6} + x^{3} x^{6} + x^{6} x^{3} + x^{6} x^{6}$

Multiply $x^{3}$ by $x^{6}$ by adding the exponents.

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

$x^{6} + x^{3 + 6} + x^{6} x^{3} + x^{6} x^{6}$

Add $3$ and $6$ .

$x^{6} + x^{9} + x^{6} x^{3} + x^{6} x^{6}$

Multiply $x^{6}$ by $x^{3}$ by adding the exponents.

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

$x^{6} + x^{9} + x^{6 + 3} + x^{6} x^{6}$

Add $6$ and $3$ .

$x^{6} + x^{9} + x^{9} + x^{6} x^{6}$

Multiply $x^{6}$ by $x^{6}$ by adding the exponents.

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

$x^{6} + x^{9} + x^{9} + x^{6 + 6}$

Add $6$ and $6$ .

$x^{6} + x^{9} + x^{9} + x^{12}$

Add $x^{9}$ and $x^{9}$ .

$x^{6} + 2 x^{9} + x^{12}$