Simplify (x^10+10y^12)^2

${(x^{10} + 10 y^{12})}^{2}$

Step 1

Rewrite ${(x^{10} + 10 y^{12})}^{2}$ as $(x^{10} + 10 y^{12}) (x^{10} + 10 y^{12})$ .

$(x^{10} + 10 y^{12}) (x^{10} + 10 y^{12})$

Step 2

Expand $(x^{10} + 10 y^{12}) (x^{10} + 10 y^{12})$ using the FOIL Method.

Apply the distributive property.

$x^{10} (x^{10} + 10 y^{12}) + 10 y^{12} (x^{10} + 10 y^{12})$

Apply the distributive property.

$x^{10} x^{10} + x^{10} (10 y^{12}) + 10 y^{12} (x^{10} + 10 y^{12})$

Apply the distributive property.

$x^{10} x^{10} + x^{10} (10 y^{12}) + 10 y^{12} x^{10} + 10 y^{12} (10 y^{12})$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x^{10}$ by $x^{10}$ by adding the exponents.

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

$x^{10 + 10} + x^{10} (10 y^{12}) + 10 y^{12} x^{10} + 10 y^{12} (10 y^{12})$

Add $10$ and $10$ .

$x^{20} + x^{10} (10 y^{12}) + 10 y^{12} x^{10} + 10 y^{12} (10 y^{12})$

Rewrite using the commutative property of multiplication.

$x^{20} + 10 x^{10} y^{12} + 10 y^{12} x^{10} + 10 y^{12} (10 y^{12})$

Rewrite using the commutative property of multiplication.

$x^{20} + 10 x^{10} y^{12} + 10 y^{12} x^{10} + 10 \cdot 10 y^{12} y^{12}$

Multiply $y^{12}$ by $y^{12}$ by adding the exponents.

Move $y^{12}$ .

$x^{20} + 10 x^{10} y^{12} + 10 y^{12} x^{10} + 10 \cdot 10 (y^{12} y^{12})$

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

$x^{20} + 10 x^{10} y^{12} + 10 y^{12} x^{10} + 10 \cdot 10 y^{12 + 12}$

Add $12$ and $12$ .

$x^{20} + 10 x^{10} y^{12} + 10 y^{12} x^{10} + 10 \cdot 10 y^{24}$

Multiply $10$ by $10$ .

$x^{20} + 10 x^{10} y^{12} + 10 y^{12} x^{10} + 100 y^{24}$

Add $10 x^{10} y^{12}$ and $10 y^{12} x^{10}$ .

Move $y^{12}$ .

$x^{20} + 10 x^{10} y^{12} + 10 x^{10} y^{12} + 100 y^{24}$

Add $10 x^{10} y^{12}$ and $10 x^{10} y^{12}$ .

$x^{20} + 20 x^{10} y^{12} + 100 y^{24}$

Step 4

Move $x^{20}$ .

$20 x^{10} y^{12} + 100 y^{24} + x^{20}$

Step 5

Reorder $20 x^{10} y^{12}$ and $100 y^{24}$ .

$100 y^{24} + 20 x^{10} y^{12} + x^{20}$