Question

*(k - 2/3)² = ?*

1️⃣ (k²- 4k/3 - 4/9)
2️⃣ (k² - 4/9)
3️⃣ (k²- 4k/3 + 4/9)
4️⃣ (k² + 4/9)​

Answer 1

$4️⃣ (k² + 4/9)$

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\displaystyle \sf{ { \bigg( k - \frac{2}{3} \bigg)}^{2} }$

1. (k²- 4k/3 - 4/9)

2. (k² - 4/9)

3. (k²- 4k/3 + 4/9)

4. (k² + 4/9)

FORMULA TO BE IMPLEMENTED

We are aware of the algebraic identity that

$\sf{ {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} }$

EVALUATION

$\displaystyle \sf{ { \bigg( k - \frac{2}{3} \bigg)}^{2} }$

$\displaystyle \sf{ = {k}^{2} - 2 \times k \times \frac{2}{3} + { \bigg( \frac{2}{3} \bigg)}^{2} }$

$\displaystyle \sf{ = {k}^{2} - \frac{4k}{3} + \frac{4}{9} }$

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf{ 3. \: \: \: \: \: {k}^{2} - \frac{4k}{3} + \frac{4}{9} }$

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