Simplify (5x+2y)^2

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

Step 1

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

$(5 x + 2 y) (5 x + 2 y)$

Step 2

Expand $(5 x + 2 y) (5 x + 2 y)$ using the FOIL Method.

Apply the distributive property.

$5 x (5 x + 2 y) + 2 y (5 x + 2 y)$

Apply the distributive property.

$5 x (5 x) + 5 x (2 y) + 2 y (5 x + 2 y)$

Apply the distributive property.

$5 x (5 x) + 5 x (2 y) + 2 y (5 x) + 2 y (2 y)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x (2 y) + 2 y (5 x) + 2 y (2 y)$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x (2 y) + 2 y (5 x) + 2 y (2 y)$

Multiply $x$ by $x$ .

$5 \cdot 5 x^{2} + 5 x (2 y) + 2 y (5 x) + 2 y (2 y)$

Multiply $5$ by $5$ .

$25 x^{2} + 5 x (2 y) + 2 y (5 x) + 2 y (2 y)$

Rewrite using the commutative property of multiplication.

$25 x^{2} + 5 \cdot 2 x y + 2 y (5 x) + 2 y (2 y)$

Multiply $5$ by $2$ .

$25 x^{2} + 10 x y + 2 y (5 x) + 2 y (2 y)$

Rewrite using the commutative property of multiplication.

$25 x^{2} + 10 x y + 2 \cdot 5 y x + 2 y (2 y)$

Multiply $2$ by $5$ .

$25 x^{2} + 10 x y + 10 y x + 2 y (2 y)$

Rewrite using the commutative property of multiplication.

$25 x^{2} + 10 x y + 10 y x + 2 \cdot 2 y \cdot y$

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

Move $y$ .

$25 x^{2} + 10 x y + 10 y x + 2 \cdot 2 (y \cdot y)$

Multiply $y$ by $y$ .

$25 x^{2} + 10 x y + 10 y x + 2 \cdot 2 y^{2}$

Multiply $2$ by $2$ .

$25 x^{2} + 10 x y + 10 y x + 4 y^{2}$

Add $10 x y$ and $10 y x$ .

Move $y$ .

$25 x^{2} + 10 x y + 10 x y + 4 y^{2}$

Add $10 x y$ and $10 x y$ .

$25 x^{2} + 20 x y + 4 y^{2}$

Simplify (5x+2y)^2

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