Chapter 10 - Section 10.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set - Page 711: 75

$(\sqrt{2x+5}-1)^{2}=2x-2\sqrt{2x+5}+6$

Work Step by Step

$(\sqrt{2x+5}-1)^{2}$ Use the formula for squaring a binomial to evaluate this power. The formula is $(a-b)^{2}=a^{2}-2ab+b^{2}$. In this expression, $a=\sqrt{2x+5}$ and $b=1$. Substitute the known values into the formula and simplify if possible: $(\sqrt{2x+5}-1)^{2}=(\sqrt{2x+5})^{2}-2\sqrt{2x+5}+1=...$ $...=2x+5-2\sqrt{2x+5}+1=...$ $...=2x-2\sqrt{2x+5}+6$

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