Question

8.4 add, subtract, and multiply radical expressions
score: 19.8/22 answered: 20/22
question 21
expand and simplify.
$(9 + 5\sqrt{2})(9 - 5\sqrt{2})=$
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Explanation:

Step1: Apply difference - of - squares formula

Use $(a + b)(a - b)=a^{2}-b^{2}$, where $a = 9$ and $b = 5\sqrt{2}$. So we have $9^{2}-(5\sqrt{2})^{2}$.

Step2: Calculate squares

$9^{2}=81$ and $(5\sqrt{2})^{2}=5^{2}\times(\sqrt{2})^{2}=25\times2 = 50$.

Step3: Subtract results

$81-50 = 31$.

Answer:

31