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multiply radical binomials (level 2)
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multiply and express in simplest radical form:
$(-4 + 2\sqrt{18})(1 + \sqrt{2})$
answer attempt 2 out of 2

Explanation:

Step1: Simplify $\sqrt{18}$

$\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$
Substitute back: $-4 + 2\times3\sqrt{2} = -4 + 6\sqrt{2}$

Step2: Apply FOIL method

Multiply $(-4 + 6\sqrt{2})(1 + \sqrt{2})$:
First terms: $-4 \times 1 = -4$
Outer terms: $-4 \times \sqrt{2} = -4\sqrt{2}$
Inner terms: $6\sqrt{2} \times 1 = 6\sqrt{2}$
Last terms: $6\sqrt{2} \times \sqrt{2} = 6\times2 = 12$

Step3: Combine like terms

Combine constant terms: $-4 + 12 = 8$
Combine radical terms: $-4\sqrt{2} + 6\sqrt{2} = 2\sqrt{2}$
Sum the results: $8 + 2\sqrt{2}$

Answer:

$8 + 2\sqrt{2}$