Question

Simplify the following expression: ( (√(6x²) + 4√(8x³))(√(9x) - x√(5x⁵)) ) assuming ( x > 0 ).

a) ( 3√(2) ⋅ √(3) ⋅ x² + 6 ⋅ x ⋅ √(2) ⋅ √(x) - √(6) ⋅ √(5) ⋅ x⁴ - 2√(10) ⋅ x⁴ )
b) ( 3√(2) ⋅ √(3) ⋅ x² - 6 ⋅ x ⋅ √(2) ⋅ √(x) + √(6) ⋅ √(5) ⋅ x⁴ + 2√(10) ⋅ x⁴ )
c) ( 3√(2) ⋅ √(3) ⋅ x² + 6 ⋅ x ⋅ √(2) ⋅ √(x) + √(6) ⋅ √(5) ⋅ x⁴ - 2√(10) ⋅ x⁴ )
d) ( -3√(2) ⋅ √(3) ⋅ x² - 6 ⋅ x ⋅ √(2) ⋅ √(x) + √(6) ⋅ √(5) ⋅ x⁴ + 2√(10) ⋅ x⁴ )

Answer 1

To simplify the expression ( (√(6x²) + 4√(8x³))(√(9x) - x√(5x⁵)) ), the final simplified expression is (3√(2)⋅√(3)⋅x² + 6⋅x⋅√(2)⋅√(x) - √(6)⋅√(5)⋅x⁴ - 2√(10)⋅x⁴).

Step-by-step explanation:

To simplify the expression ( (√(6x²) + 4√(8x³))(√(9x) - x√(5x⁵)) ), we can start by simplifying each term individually. The square root of a number can be simplified by factoring out any perfect square factors. For instance, √(6x²) can be rewritten as √(3x²)⋅√(2). Applying this rule to each term and simplifying further, we get (3√(2)⋅√(3)⋅x² + 6⋅x⋅√(2)⋅√(x) - √(6)⋅√(5)⋅x⁴ - 2√(10)⋅x⁴) as the final simplified expression.