Question

multiply: \\((\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8})\\)

-22
-246
\\(10 - 8\sqrt{2}\\)
\\(10 + 8\sqrt{2}\\)

multiply: \\((\sqrt{2x^3} + \sqrt{12x})(2\sqrt{10x^5} + \sqrt{6x^2})\\)

\\(2\sqrt{10x^4} + 2\sqrt{3x^3} + 4\sqrt{15x^3} + 6\sqrt{2x}\\)
\\(2x^2\sqrt{5} + 2x\sqrt{3x} + 2x^3\sqrt{30} + 3x\sqrt{2x}\\)
\\(4x^4\sqrt{5} + 2x^2\sqrt{3x} + 4x^3\sqrt{30} + 6x\sqrt{2x}\\)
\\(x^4\sqrt{20} + x^2\sqrt{6x} + x^3\sqrt{120} + x\sqrt{12x}\\)

Explanation:

Multiply conjugate binomial radicals

Using the Radical Conjugates and Multiplying Binomial Radicals knowledge points

$$
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Expand the second binomial product

Using the Distributive Property and Multiplying Binomial Radicals knowledge points

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$$

Simplify each term in the expansion

Using the Product Property of Radicals and Simplifying Radical Products knowledge points

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$$

Combine the simplified terms

Using the Simplifying Radical Products knowledge point

$$ P = 4x^4\sqrt{5} + 2x^2\sqrt{3x} + 4x^3\sqrt{30} + 6x\sqrt{2x} $$

Answer:

Question 1

• (A) -22 (Correct answer)
• (B) -246
• (C) \(10-8\sqrt{2}\)
• (D) \(10+8\sqrt{2}\)

Question 2

• (A) \(2\sqrt{10}x^4 + 2\sqrt{3x^3} + 4\sqrt{15x^3} + 6\sqrt{2x}\)
• (B) \(2x^2\sqrt{5} + 2x\sqrt{3x} + 2x^3\sqrt{30} + 3x\sqrt{2x}\)
• (C) \(4x^4\sqrt{5} + 2x^2\sqrt{3x} + 4x^3\sqrt{30} + 6x\sqrt{2x}\) (Correct answer)
• (D) \(x^4\sqrt{20} + x^2\sqrt{6x} + x^3\sqrt{120} + x\sqrt{12x}\)