QuestionJuly 14, 2025

2 Essay 0.5 points Explain why the computational result in the following is wrong and give the correct answer. (x+h)^2=x^2+h^2

2 Essay 0.5 points Explain why the computational result in the following is wrong and give the correct answer. (x+h)^2=x^2+h^2
2 Essay 0.5 points Explain why the computational result in the following is wrong and give the correct answer. (x+h)^2=x^2+h^2

Solution
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Answer

x^2 + 2xh + h^2 Explanation 1. Identify the Error The expression (x+h)^2 is incorrectly expanded as x^2 + h^2. This ignores the middle term in the binomial expansion. 2. Apply Binomial Expansion Use the formula **(a+b)^2 = a^2 + 2ab + b^2**. Here, a = x and b = h. 3. Correct the Expansion Substitute into the formula: (x+h)^2 = x^2 + 2xh + h^2.

Explanation

1. Identify the Error<br /> The expression $(x+h)^2$ is incorrectly expanded as $x^2 + h^2$. This ignores the middle term in the binomial expansion.<br />2. Apply Binomial Expansion<br /> Use the formula **$(a+b)^2 = a^2 + 2ab + b^2$**. Here, $a = x$ and $b = h$.<br />3. Correct the Expansion<br /> Substitute into the formula: $(x+h)^2 = x^2 + 2xh + h^2$.
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