Algebra Examples

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

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify the expression.

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Step 1.2.1

Multiply $- 4$ by $2$ .

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

Step 1.2.2

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

$2 m (2 m) + 2 m (- 8 n) - 8 n (2 m - 8 n)$

Step 2.3

Apply the distributive property.

$2 m (2 m) + 2 m (- 8 n) - 8 n (2 m) - 8 n (- 8 n)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

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

Step 3.1.2

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

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Step 3.1.2.1

Move $m$ .

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

Step 3.1.2.2

Multiply $m$ by $m$ .

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

Step 3.1.3

Multiply $2$ by $2$ .

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

Step 3.1.4

Rewrite using the commutative property of multiplication.

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

Step 3.1.5

Multiply $2$ by $- 8$ .

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

Step 3.1.6

Rewrite using the commutative property of multiplication.

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

Step 3.1.7

Multiply $- 8$ by $2$ .

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

Step 3.1.8

Rewrite using the commutative property of multiplication.

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

Step 3.1.9

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

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Step 3.1.9.1

Move $n$ .

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

Step 3.1.9.2

Multiply $n$ by $n$ .

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

Step 3.1.10

Multiply $- 8$ by $- 8$ .

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

Step 3.2

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

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Step 3.2.1

Move $n$ .

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

Step 3.2.2

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

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