Question

Mitultiply: (√2x³+√12x) (2√10x^5+ √6x²

O 2√10x +2√3x³ +4√15x³ +6√/2x
O 2x²√√5 +2x√3x + 2x³√30+3x√2x
4x√√5+2x²√√3x +4x³√√30 +6x√2x
x√20+x²√√6x + x³√120+x√12x
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Answer 1

To multiply the given expressions, we can simplify each term, multiply the coefficients, and combine like terms. The product is 4x^4√5 + 4x^3√30 + 2x^2√3 + 6x√2x.

Step-by-step explanation:

To multiply two expressions, we can use the distributive property. In this case, we have two square root terms multiplied by two square root terms. To simplify, we can combine like terms, multiply the coefficients, and apply the exponent rules.

Let's break down the given expression step by step:

1. Multiply the coefficients: (1 * 2) = 2
2. Multiply the square root terms:
   • (√2x³) * (2√10x^5) = 2√(2 * 10 * x^3 * x^5) = 2√(20x^8) = 2 * 2x^4 * √5 = 4x^4√5
   • (√12x) * (2√10x^5) = 2√(12 * 10 * x * x^5) = 2√(120x^6) = 2 * 2√(30 * x^3 * x^3) = 4x^3√30
   • (√2x³) * (√6x²) = √(2 * 6 * x^3 * x^2) = √(12x^5) = √(3 * 2 * x^3 * x^2) = 2x^2√3
   • (√12x) * (√6x²) = √(12 * 6 * x * x^2) = √(72x^3) = √(12 * 6 * x^2 * x) = 2x√(18 * x) = 2x√(9 * 2 * x) = 2x √9 * √(2 * x) = 2x * 3 * √2x = 6x√2x
3. Combine the simplified terms:
   • 4x^4√5 + 4x^3√30 + 2x^2√3 + 6x√2x

Therefore, the product of the given expressions is 4x^4√5 + 4x^3√30 + 2x^2√3 + 6x√2x.