multiply radical binomials (level 2)
score: 3/5 penalty: 1 off
question
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multiply and express in simplest radical form:
(4 + 2√63)(4 − √7)

Question

multiply radical binomials (level 2)
score: 3/5  penalty: 1 off
question
watch video  show examples
multiply and express in simplest radical form:
(4 + 2√63)(4 − √7)

Accepted Answer

# Explanation:
## Step1: Simplify $\sqrt{63}$
$\sqrt{63}=\sqrt{9\times7}=3\sqrt{7}$
So the expression becomes $(4 + 2\times3\sqrt{7})(4-\sqrt{7})=(4 + 6\sqrt{7})(4-\sqrt{7})$
## Step2: Use the FOIL method
$$
\begin{align*}
&(4 + 6\sqrt{7})(4-\sqrt{7})\
=&4\times4-4\times\sqrt{7}+6\sqrt{7}\times4-6\sqrt{7}\times\sqrt{7}\
=&16-4\sqrt{7}+24\sqrt{7}-6\times7
\end{align*}
$$
## Step3: Combine like - terms
$$
\begin{align*}
&16-4\sqrt{7}+24\sqrt{7}-42\
=&(16 - 42)+(-4\sqrt{7}+24\sqrt{7})\
=&-26 + 20\sqrt{7}
\end{align*}
$$

# Answer:
$-26 + 20\sqrt{7}$

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QUESTION IMAGE

Question

Explanation:

Step1: Simplify \(\sqrt{63}\)

Step2: Use the FOIL method

Step3: Combine like - terms

Answer: