Question
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Answer
The product is \(4x^2 + 8x + 4\).
Solution
1. Recognize that the square of a binomial is given by
\[
(a+b)^2 = a^2 + 2ab + b^2.
\]
2. In the expression \((2x+2)^2\), let
\[
a = 2x \quad \text{and} \quad b = 2.
\]
3. Compute each term:
- \(a^2 = (2x)^2 = 4x^2\),
- \(2ab = 2\cdot (2x)\cdot 2 = 8x\),
- \(b^2 = 2^2 = 4\).
4. Combine the results:
\[
(2x+2)^2 = 4x^2 + 8x + 4.
\]
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Simplify this solution The Deep Dive
To find the product of \( (2x + 2)^2 \), we will use the formula for the square of a binomial, which states that \( (a + b)^2 = a^2 + 2ab + b^2 \). Here, let \( a = 2x \) and \( b = 2 \). Now, applying the formula: 1. Square \( a \): \( (2x)^2 = 4x^2 \) 2. Square \( b \): \( 2^2 = 4 \) 3. Calculate \( 2ab \): \( 2 \cdot (2x) \cdot 2 = 8x \) Putting it all together: \[ (2x+2)^2 = 4x^2 + 8x + 4 \] So, the final result is: \[ \boxed{4x^2 + 8x + 4} \]
