Respuesta :

We know that :

✿  (p - q)² = (p)² - 2(p)(q) + (q)²

The Given Problem is in the Same Form

Where :

✿  [tex]\mathsf{p = (3 + \frac{a}{4})}[/tex]

✿  [tex]\mathsf{q = (1 + \frac{a}{4})}[/tex]

[tex]\mathsf{\implies (3 + \frac{a}{4})^2 - 2(3 + \frac{a}{4})(1 + \frac{a}{4}) + (1 + \frac{a}{4})^2 = [(3 + \frac{a}{4}) - (1 + \frac{a}{4})]^2}[/tex]

[tex]\mathsf{\implies (3 + \frac{a}{4})^2 - 2(3 + \frac{a}{4})(1 + \frac{a}{4}) + (1 + \frac{a}{4})^2 = [(3 + \frac{a}{4} - 1 - \frac{a}{4})]^2}[/tex]

[tex]\mathsf{\implies (3 + \frac{a}{4})^2 - 2(3 + \frac{a}{4})(1 + \frac{a}{4}) + (1 + \frac{a}{4})^2 = [(3 - 1)]^2}[/tex]

[tex]\mathsf{\implies (3 + \frac{a}{4})^2 - 2(3 + \frac{a}{4})(1 + \frac{a}{4}) + (1 + \frac{a}{4})^2 = [2]^2}[/tex]

[tex]\mathsf{\implies (3 + \frac{a}{4})^2 - 2(3 + \frac{a}{4})(1 + \frac{a}{4}) + (1 + \frac{a}{4})^2 = 4}[/tex]

Answer:

4

Step-by-step explanation:

( 3 + 1/4 a)^2 - 2 ( 3 + 1/4 a)(1 + 1/4 a) + (1+ 1/4 a)^2

= 9 + 3/2 a + 1/16 a^2 - 2( 3 + 3/4 a + 1/4 a + 1/16 a^2) + 1 + 1/2 a + 1/16 a^2

= 9 + 3/2 a + 1/16 a^2 - 6 - 3/2 a - 1/2 a - 1/8a^2 + 1 + 1/2 a + 1/16 a^2

= 4   (answer)