Question

DISCUSS: An Algebra Error Beginning algebra students sometimes make the following error when squaring a binomial: $$(x+5)^{2}=x^{2}+25$$ (a) Substitute a value for $x$ to verify that this is an error. (b) What is the correct expansion for $(x+5)^{2} ?$

   DISCUSS: An Algebra Error Beginning algebra students
sometimes make the following error when squaring a binomial:
$$(x+5)^{2}=x^{2}+25$$
(a) Substitute a value for $x$ to verify that this is an error.
(b) What is the correct expansion for $(x+5)^{2} ?$

Algebra and Trigonometry

James Stewart,… 4th Edition

Chapter 0, Problem 93

Instant Answer

Solved by Expert M S

07/02/2019

Step 1

We can do this by substituting a value for $x$. Let's choose $x=1$. Substituting $x=1$ into the equation, we get $(1+5)^{2}$ on the left side and $1^{2}+25$ on the right side. Simplifying, we get $36$ on the left side and $26$ on the right side. Since $36$ is not Show more…

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DISCUSS: An Algebra Error Beginning algebra students sometimes make the following error when squaring a binomial: $$(x+5)^{2}=x^{2}+25$$ (a) Substitute a value for $x$ to verify that this is an error. (b) What is the correct expansion for $(x+5)^{2} ?$

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Key Concepts

Error Verification via Substitution

This concept is about using numerical substitution to test whether an algebraic manipulation or expansion is correct. By substituting a specific value for the variable in both the original and the expanded expressions and comparing the results, one can quickly identify mistakes in the algebraic process. This technique is a valuable tool for validating the correctness of algebraic operations.

Binomial Expansion

This concept involves expanding an expression that is the power of a binomial. It specifically includes recognizing and applying the formula (a + b)² = a² + 2ab + b², which ensures that all necessary terms, including the product of the two distinct terms multiplied by two, are correctly accounted for. Understanding this concept prevents common errors when working with polynomial expressions.

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