Answered

Format the following question or task so that it is easier to read.
Fix any grammar or spelling errors.
Remove phrases that are not part of the question.
Do not remove or change LaTeX formatting.
Do not change or remove [tex] [/tex] tags.
If the question is nonsense, rewrite it so that it makes sense.
-----
[tex]$(x / 2+3 / 4)^2=$[/tex]
-----

Response:

Simplify the expression:

[tex]\[ \left( \frac{x}{2} + \frac{3}{4} \right)^2 \][/tex]



Answer :

GinnyAnswer
To solve the expression [tex]\((\frac{x}{2} + \frac{3}{4})^2\)[/tex], we need to expand it step by step.

First, we can recognize that [tex]\((a + b)^2\)[/tex] follows the formula:

[tex]\[ (a + b)^2 = a^2 + 2ab + b^2 \][/tex]

In our case, [tex]\(a = \frac{x}{2}\)[/tex] and [tex]\(b = \frac{3}{4}\)[/tex]. Plugging these into the formula, we get:

[tex]\[ \left(\frac{x}{2} + \frac{3}{4}\right)^2 = \left(\frac{x}{2}\right)^2 + 2 \left(\frac{x}{2}\right) \left(\frac{3}{4}\right) + \left(\frac{3}{4}\right)^2 \][/tex]

Now, let's compute each term separately:

1. [tex]\(\left(\frac{x}{2}\right)^2\)[/tex]:

[tex]\[ \left(\frac{x}{2}\right)^2 = \frac{x^2}{4} = 0.25x^2 \][/tex]

2. [tex]\(2 \left(\frac{x}{2}\right) \left(\frac{3}{4}\right)\)[/tex]:

[tex]\[ 2 \left(\frac{x}{2}\right) \left(\frac{3}{4}\right) = 2 \cdot \frac{x}{2} \cdot \frac{3}{4} = \frac{3x}{4} = 0.75x \][/tex]

3. [tex]\(\left(\frac{3}{4}\right)^2\)[/tex]:

[tex]\[ \left(\frac{3}{4}\right)^2 = \frac{9}{16} = 0.5625 \][/tex]

Now, we can combine all the computed terms:

[tex]\[ \left(\frac{x}{2} + \frac{3}{4}\right)^2 = 0.25x^2 + 0.75x + 0.5625 \][/tex]

Therefore, the expanded form of [tex]\((\frac{x}{2} + \frac{3}{4})^2\)[/tex] is:

[tex]\[ 0.25x^2 + 0.75x + 0.5625 \][/tex]

Other Questions