Write in Standard Form (4m+n)(m-2n)

$(4 m + n) (m - 2 n)$

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

Expand $(4 m + n) (m - 2 n)$ using the FOIL Method.

Apply the distributive property.

$4 m (m - 2 n) + n (m - 2 n)$

Apply the distributive property.

$4 m \cdot m + 4 m (- 2 n) + n (m - 2 n)$

Apply the distributive property.

$4 m \cdot m + 4 m (- 2 n) + n m + n (- 2 n)$

Step 3

Simplify and combine like terms.

Simplify each term.

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

Move $m$ .

$4 (m \cdot m) + 4 m (- 2 n) + n m + n (- 2 n)$

Multiply $m$ by $m$ .

$4 m^{2} + 4 m (- 2 n) + n m + n (- 2 n)$

Rewrite using the commutative property of multiplication.

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

Multiply $4$ by $- 2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

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

Multiply $n$ by $n$ .

$4 m^{2} - 8 m n + n m - 2 n^{2}$

Add $- 8 m n$ and $n m$ .

Reorder $n$ and $m$ .

$4 m^{2} - 8 m n + m n - 2 n^{2}$

Add $- 8 m n$ and $m n$ .

$4 m^{2} - 7 m n - 2 n^{2}$