Questions: Simplify the following expression. (5x+2)^2

Transcript text: Simplify the following expression. \[ (5 x+2)^{2} \]

Solution

Solution Steps

To simplify the given expression \((5x + 2)^2\), we can use the binomial expansion formula \((a + b)^2 = a^2 + 2ab + b^2\). Here, \(a = 5x\) and \(b = 2\). We will expand the expression using this formula.

Step 1: Identify the Binomial Expansion Formula

To simplify the expression \((5x + 2)^2\), we use the binomial expansion formula: \[ (a + b)^2 = a^2 + 2ab + b^2 \] Here, \(a = 5x\) and \(b = 2\).

Step 2: Apply the Binomial Expansion Formula

Substitute \(a\) and \(b\) into the formula: \[ (5x + 2)^2 = (5x)^2 + 2 \cdot (5x) \cdot 2 + 2^2 \]

Step 3: Simplify Each Term

Calculate each term separately: \[ (5x)^2 = 25x^2 \] \[ 2 \cdot (5x) \cdot 2 = 20x \] \[ 2^2 = 4 \]

Step 4: Combine the Terms

Combine all the simplified terms: \[ (5x + 2)^2 = 25x^2 + 20x + 4 \]

Final Answer

\[ \boxed{25x^2 + 20x + 4} \]

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