Question

${( \frac{1}{2} x + 1)}^{2}$
please answer the question
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Answer 1

QUESTION :-

Evaluate : $(\frac{1}{2} x + 1)^2$

SOLUTION :-

Using the Algebraic Identity, $(a + b)^2 = a^2 + 2ab + b^2$

where, a = $\frac{1}{2} x$ ; b = 1

$(\frac{1}{2} x + 1)^2 = (\frac{1}{2}x)^2 + 2 (\frac{1}{2} )(1) + 1^2\\\\\Rightarrow \frac{1}{4} x^2 + 1 + 1\\\\= \bold {\frac{1}{4} x^2 + 2}$

CONCLUSION :-

$\bold {(\frac{1}{2} x + 1)^2 = \frac{1}{4} x^2 + 2}$