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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

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Exercise 61 Page 62

Consider a binomial where both terms are positive.

False. The binomial a^2+b^2 cannot be factored.

Practice makes perfect

We are given the following statement. All binomials that have a perfect square in each of the two terms can be factored.

If we consider the difference of two perfect squares, then it can be factored. a^2-b^2 = (a+b)(a-b) However, if we consider the sum of two perfect squares, it cannot be factored. a^2+b^2 The above expression is a counterexample to the given statement. Thus, it is false.

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Exercises p.60-63