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Problem 93 Hard Difficulty

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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Video Transcript

pillow. Beginning algebra, students sometimes make the following error when square, they square the first term, then square the second term and just atoms together. However, they miss an important step called boiling, which I will show you in part B. But first, let's substitute a value in for X to verify the year. So let's say X equals one. So one plus far parentheses squared and one squared plus 25 one plus five equals six squared and one squared. It was one less 25. Six squared equals 36 in one place, 25 equals. No. 36 is not equal 26. So that shows that this myth that is incorrect. Part B We were correctly expand using the boiling method. So falling means first outer inner. Unless so, we have explicit fun Times X plus five. So do the first terms, which will be X and X x times x X squared noted outside time. So EXT. Time Spy, which is five X and the road positive. So plus, now you do the inside terms, except by I want to be five x also in night of the last times five times, but which equals 25. And lastly, you combine like terms. So you look at matching degrees and the only ones here is this. Five X In this five picks and five plus five equals 10. They have X squared those tunics close to 25 in the agency.

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Video Transcript

James Stewart, Lothar Redlin, Saleem Watson

Algebra and Trigonometry

Grace He

Catherine Ross

Caleb Elmore

Kristen Karbon

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Algebra and Trigonometry

Grace He

Catherine Ross

Caleb Elmore

Kristen Karbon

James Stewart, Lothar Redlin, Saleem WatsonAlgebra and Trigonometry

Grace He

Catherine Ross

Caleb Elmore

Kristen Karbon

James Stewart, Lothar Redlin, Saleem Watson

Algebra and Trigonometry