Find the Product (x-5y)^2

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

Step 1

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

$(x - 5 y) (x - 5 y)$

Step 2

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

Apply the distributive property.

$x (x - 5 y) - 5 y (x - 5 y)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

$x^{2} - 5 x y - 5 y x - 5 \cdot - 5 y \cdot y$

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

Move $y$ .

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

Multiply $y$ by $y$ .

$x^{2} - 5 x y - 5 y x - 5 \cdot - 5 y^{2}$

Multiply $- 5$ by $- 5$ .

$x^{2} - 5 x y - 5 y x + 25 y^{2}$

Subtract $5 y x$ from $- 5 x y$ .

Move $y$ .

$x^{2} - 5 x y - 5 x y + 25 y^{2}$

Subtract $5 x y$ from $- 5 x y$ .

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