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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Step 1
Let's let \(x = 2\). Substitute \(x = 2\) into the incorrect equation: \((2+5)^{2} = 2^{2} + 25\) \(7^{2} = 4 + 25\) \(49 \neq 29\) ** 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 $(x+5)^{2} ?$
Prerequisites
Algebraic Expressions
Find the error in the following work. $$\begin{aligned} D_{x}\left(\frac{2 x+5}{x^{2}-1}\right) &=\frac{(2 x+5)(2 x)-\left(x^{2}-1\right) 2}{\left(x^{2}-1\right)^{2}} \\ &=\frac{4 x^{2}+10 x-2 x^{2}+2}{\left(x^{2}-1\right)^{2}} \\ &=\frac{2 x^{2}+10 x+2}{\left(x^{2}-1\right)^{2}} \end{aligned}$$
Calculating the Derivative
Derivatives of Products and Quotients
Describe and correct the error in using the Pythagorean Theorem $c^{2} \square a^{2}+b^{2}$ $x^{2} \square 10^{2}+26^{2}$ $x^{2} \square 100+676$ $x^{2} \square 776$ $x \square \sqrt{776}$ $x \approx 27.9$
Right Triangles and Trigonometry
The Pythagorean Theorem
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