Write in Standard Form (x-4y)^2

${(x - 4 y)}^{2}$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Rewrite ${(x - 4 y)}^{2}$ as $(x - 4 y) (x - 4 y)$ .

$(x - 4 y) (x - 4 y)$

Expand $(x - 4 y) (x - 4 y)$ using the FOIL Method.

Apply the distributive property.

$x (x - 4 y) - 4 y (x - 4 y)$

Apply the distributive property.

$x \cdot x + x (- 4 y) - 4 y (x - 4 y)$

Apply the distributive property.

$x \cdot x + x (- 4 y) - 4 y x - 4 y (- 4 y)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x (- 4 y) - 4 y x - 4 y (- 4 y)$

Rewrite using the commutative property of multiplication.

$x^{2} - 4 x y - 4 y x - 4 y (- 4 y)$

Rewrite using the commutative property of multiplication.

$x^{2} - 4 x y - 4 y x - 4 \cdot - 4 y \cdot y$

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

Move $y$ .

$x^{2} - 4 x y - 4 y x - 4 \cdot - 4 (y \cdot y)$

Multiply $y$ by $y$ .

$x^{2} - 4 x y - 4 y x - 4 \cdot - 4 y^{2}$

Multiply $- 4$ by $- 4$ .

$x^{2} - 4 x y - 4 y x + 16 y^{2}$

Subtract $4 y x$ from $- 4 x y$ .

Move $y$ .

$x^{2} - 4 x y - 4 x y + 16 y^{2}$

Subtract $4 x y$ from $- 4 x y$ .

$x^{2} - 8 x y + 16 y^{2}$