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Chapter 0: Problem 42

Find each product. $$(x+5)^{2}$$

Short Answer

Expert verified
Hence, the product of the given expression \((x + 5)^2\) is \(x^2 + 10x + 25\).

Step by step solution

01

Identify the binomial expression

The binomial expression given is \((x + 5)^2\).
02

Apply the formula

Apply the special expansion formula for \((x + a)^2\), which is \((x + a)^2 = x^2 + 2ax + a^2\). Here, \(a=5\). Substituting these values into the formula gives \(x^2 + 2(5)x + (5)^2\).
03

Simplify the expression

Simplify \(2(5)x\) and \((5)^2\) to get \(10x\) and \(25\) respectively. Therefore, the expanded and simplified expression is \(x^2 + 10x + 25\).

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