Write in Standard Form (2m-8)^2

${(2 m - 8)}^{2}$

Step 1

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

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

Step 2

Rewrite ${(2 m - 8)}^{2}$ as $(2 m - 8) (2 m - 8)$ .

$(2 m - 8) (2 m - 8)$

Step 3

Expand $(2 m - 8) (2 m - 8)$ using the FOIL Method.

Apply the distributive property.

$2 m (2 m - 8) - 8 (2 m - 8)$

Apply the distributive property.

$2 m (2 m) + 2 m \cdot - 8 - 8 (2 m - 8)$

Apply the distributive property.

$2 m (2 m) + 2 m \cdot - 8 - 8 (2 m) - 8 \cdot - 8$

Step 4

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 m \cdot m + 2 m \cdot - 8 - 8 (2 m) - 8 \cdot - 8$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$2 \cdot 2 (m \cdot m) + 2 m \cdot - 8 - 8 (2 m) - 8 \cdot - 8$

Multiply $m$ by $m$ .

$2 \cdot 2 m^{2} + 2 m \cdot - 8 - 8 (2 m) - 8 \cdot - 8$

Multiply $2$ by $2$ .

$4 m^{2} + 2 m \cdot - 8 - 8 (2 m) - 8 \cdot - 8$

Multiply $- 8$ by $2$ .

$4 m^{2} - 16 m - 8 (2 m) - 8 \cdot - 8$

Multiply $2$ by $- 8$ .

$4 m^{2} - 16 m - 16 m - 8 \cdot - 8$

Multiply $- 8$ by $- 8$ .

$4 m^{2} - 16 m - 16 m + 64$

Subtract $16 m$ from $- 16 m$ .

$4 m^{2} - 32 m + 64$