Expand and siplify `(x +4) ^(2) + (x-2) ^(2)`

Options

A. `2 (x2 + 2x + 10)`
B. ` 2 (x2 + 2x - 10)`
C. `2 (x2 - 2x + 10)`
D. `2 (x e - 2x - 10)`

Answer

To expand and simplify the expression \((x + 4)^2 + (x - 2)^2\), we can follow these steps:

### Step 1: Expand \((x + 4)^2\)
Using the formula \((a + b)^2 = a^2 + 2ab + b^2\), we have:
\[ (x + 4)^2 = x^2 + 2(x)(4) + 4^2 = x^2 + 8x + 16 \]

### Step 2: Expand \((x - 2)^2\)
Using the formula \((a - b)^2 = a^2 - 2ab + b^2\), we have:
\[ (x - 2)^2 = x^2 - 2(x)(2) + 2^2 = x^2 - 4x + 4 \]

### Step 3: Combine the expanded forms
Now we add the two expanded expressions:
\[ (x + 4)^2 + (x - 2)^2 = (x^2 + 8x + 16) + (x^2 - 4x + 4) \]

### Step 4: Simplify the expression
Combine like terms:
\[ = x^2 + x^2 + 8x - 4x + 16 + 4 \]
\[ = 2x^2 + 4x + 20 \]

### Final Result
Thus, the expanded and simplified form of \((x + 4)^2 + (x - 2)^2\) is:
\[ 2x^2 + 4x + 20 \]

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