Basic Math Examples

{(4 k - 2)}^{2}

${(4 k - 2)}^{2}$

Step 1

Rewrite

{(4 k - 2)}^{2}

${(4 k - 2)}^{2}$ as

(4 k - 2) (4 k - 2)

$(4 k - 2) (4 k - 2)$ .

(4 k - 2) (4 k - 2)

$(4 k - 2) (4 k - 2)$

Step 2

Expand

(4 k - 2) (4 k - 2)

$(4 k - 2) (4 k - 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

4 k (4 k - 2) - 2 (4 k - 2)

$4 k (4 k - 2) - 2 (4 k - 2)$

Step 2.2

Apply the distributive property.

4 k (4 k) + 4 k \cdot - 2 - 2 (4 k - 2)

$4 k (4 k) + 4 k \cdot - 2 - 2 (4 k - 2)$

Step 2.3

Apply the distributive property.

4 k (4 k) + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2

$4 k (4 k) + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2$

4 k (4 k) + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2

$4 k (4 k) + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2$

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.

4 \cdot 4 k \cdot k + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2

$4 \cdot 4 k \cdot k + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2$

Step 3.1.2

Multiply

k

$k$ by

k

$k$ by adding the exponents.

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Step 3.1.2.1

Move

k

$k$ .

4 \cdot 4 (k \cdot k) + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2

$4 \cdot 4 (k \cdot k) + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2$

Step 3.1.2.2

Multiply

k

$k$ by

k

$k$ .

4 \cdot 4 k^{2} + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2

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

4 \cdot 4 k^{2} + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2

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

Step 3.1.3

Multiply

4

$4$ by

4

$4$ .

16 k^{2} + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2

$16 k^{2} + 4 k \cdot - 2 - 2 (4 k) - 2 \cdot - 2$

Step 3.1.4

Multiply

- 2

$- 2$ by

4

$4$ .

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

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

Step 3.1.5

Multiply

4

$4$ by

- 2

$- 2$ .

16 k^{2} - 8 k - 8 k - 2 \cdot - 2

$16 k^{2} - 8 k - 8 k - 2 \cdot - 2$

Step 3.1.6

Multiply

- 2

$- 2$ by

- 2

$- 2$ .

16 k^{2} - 8 k - 8 k + 4

$16 k^{2} - 8 k - 8 k + 4$

16 k^{2} - 8 k - 8 k + 4

$16 k^{2} - 8 k - 8 k + 4$

Step 3.2

Subtract

8 k

$8 k$ from

- 8 k

$- 8 k$ .

16 k^{2} - 16 k + 4

$16 k^{2} - 16 k + 4$

16 k^{2} - 16 k + 4

$16 k^{2} - 16 k + 4$