Simplify (10x+10y)(10x+10y)

$(10 x + 10 y) (10 x + 10 y)$

Step 1

Expand $(10 x + 10 y) (10 x + 10 y)$ using the FOIL Method.

Apply the distributive property.

$10 x (10 x + 10 y) + 10 y (10 x + 10 y)$

Apply the distributive property.

$10 x (10 x) + 10 x (10 y) + 10 y (10 x + 10 y)$

Apply the distributive property.

$10 x (10 x) + 10 x (10 y) + 10 y (10 x) + 10 y (10 y)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$10 \cdot 10 x \cdot x + 10 x (10 y) + 10 y (10 x) + 10 y (10 y)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$10 \cdot 10 (x \cdot x) + 10 x (10 y) + 10 y (10 x) + 10 y (10 y)$

Multiply $x$ by $x$ .

$10 \cdot 10 x^{2} + 10 x (10 y) + 10 y (10 x) + 10 y (10 y)$

Multiply $10$ by $10$ .

$100 x^{2} + 10 x (10 y) + 10 y (10 x) + 10 y (10 y)$

Rewrite using the commutative property of multiplication.

$100 x^{2} + 10 \cdot 10 x y + 10 y (10 x) + 10 y (10 y)$

Multiply $10$ by $10$ .

$100 x^{2} + 100 x y + 10 y (10 x) + 10 y (10 y)$

Rewrite using the commutative property of multiplication.

$100 x^{2} + 100 x y + 10 \cdot 10 y x + 10 y (10 y)$

Multiply $10$ by $10$ .

$100 x^{2} + 100 x y + 100 y x + 10 y (10 y)$

Rewrite using the commutative property of multiplication.

$100 x^{2} + 100 x y + 100 y x + 10 \cdot 10 y \cdot y$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$100 x^{2} + 100 x y + 100 y x + 10 \cdot 10 (y \cdot y)$

Multiply $y$ by $y$ .

$100 x^{2} + 100 x y + 100 y x + 10 \cdot 10 y^{2}$

Multiply $10$ by $10$ .

$100 x^{2} + 100 x y + 100 y x + 100 y^{2}$

Add $100 x y$ and $100 y x$ .

Move $y$ .

$100 x^{2} + 100 x y + 100 x y + 100 y^{2}$

Add $100 x y$ and $100 x y$ .

$100 x^{2} + 200 x y + 100 y^{2}$