Question
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Answer
The product is \( 25x^2 + 10x + 1 \).
Solution
Let’s expand \( (5x+1)^2 \) step by step.
1. Write the expression as a product:
\[
(5x+1)^2 = (5x+1)(5x+1)
\]
2. Use the distributive property (FOIL method):
\[
(5x+1)(5x+1) = (5x)(5x) + (5x)(1) + (1)(5x) + (1)(1)
\]
3. Multiply each term:
\[
= 25x^2 + 5x + 5x + 1
\]
4. Combine like terms:
\[
= 25x^2 + 10x + 1
\]
The final expanded product is:
\[
25x^2 + 10x + 1
\]
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Simplify this solution Beyond the Answer
To find the product of \((5x + 1)^2\), we can use the formula for the square of a binomial, \((a + b)^2 = a^2 + 2ab + b^2\). Here, \(a = 5x\) and \(b = 1\). Calculating step by step: 1. Calculate \(a^2\): \((5x)^2 = 25x^2\) 2. Calculate \(2ab\): \(2 \cdot (5x) \cdot 1 = 10x\) 3. Calculate \(b^2\): \(1^2 = 1\) Now, putting it all together: \[ (5x + 1)^2 = 25x^2 + 10x + 1 \] So, the product is: \[ \boxed{25x^2 + 10x + 1} \]
