Expand the Trigonometric Expression (2s+o-4n)^2

${(2 s + o - 4 n)}^{2}$

Step 1

Rewrite ${(2 s + o - 4 n)}^{2}$ as $(2 s + o - 4 n) (2 s + o - 4 n)$ .

$(2 s + o - 4 n) (2 s + o - 4 n)$

Step 2

Expand $(2 s + o - 4 n) (2 s + o - 4 n)$ by multiplying each term in the first expression by each term in the second expression.

$2 s (2 s) + 2 s o + 2 s (- 4 n) + o (2 s) + o \cdot o + o (- 4 n) - 4 n (2 s) - 4 n o - 4 n (- 4 n)$

Step 3

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 s \cdot s + 2 s o + 2 s (- 4 n) + o (2 s) + o \cdot o + o (- 4 n) - 4 n (2 s) - 4 n o - 4 n (- 4 n)$

Multiply $s$ by $s$ by adding the exponents.

Move $s$ .

$2 \cdot 2 (s \cdot s) + 2 s o + 2 s (- 4 n) + o (2 s) + o \cdot o + o (- 4 n) - 4 n (2 s) - 4 n o - 4 n (- 4 n)$

Multiply $s$ by $s$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 4$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $o$ by $o$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 4$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $n$ .

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

Multiply $n$ by $n$ .

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

Multiply $- 4$ by $- 4$ .

$4 s^{2} + 2 s o - 8 s n + 2 o s + o^{2} - 4 o n - 8 n s - 4 n o + 16 n^{2}$

Step 4

Add $2 s o$ and $2 o s$ .

Move $s$ .

$4 s^{2} + 2 o s + 2 o s - 8 s n + o^{2} - 4 o n - 8 n s - 4 n o + 16 n^{2}$

Add $2 o s$ and $2 o s$ .

$4 s^{2} + 4 o s - 8 s n + o^{2} - 4 o n - 8 n s - 4 n o + 16 n^{2}$

Step 5

Subtract $8 n s$ from $- 8 s n$ .

Move $s$ .

$4 s^{2} + 4 o s + o^{2} - 4 o n - 8 n s - 8 n s - 4 n o + 16 n^{2}$

Subtract $8 n s$ from $- 8 n s$ .

$4 s^{2} + 4 o s + o^{2} - 4 o n - 16 n s - 4 n o + 16 n^{2}$

Step 6

Subtract $4 n o$ from $- 4 o n$ .

Move $o$ .

$4 s^{2} + 4 o s + o^{2} - 4 n o - 4 n o - 16 n s + 16 n^{2}$

Subtract $4 n o$ from $- 4 n o$ .

$4 s^{2} + 4 o s + o^{2} - 8 n o - 16 n s + 16 n^{2}$

Expand the Trigonometric Expression (2s+o-4n)^2

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