Final answer:
To multiply the radical expression 2√3x(2x√15x + 3√60x³), distribute the term outside the parentheses across each term inside, yielding 4x√45x² + 6√180x⁴.
Step-by-step explanation:
The question is asking how to multiply the following radical expression: 2√3x(2x√15x + 3√60x³). To approach this, we distribute the term outside the parentheses across each term inside the parentheses.
Multiply 2√3x and 2x√15x: 2x2 is 4, and √3x×√15x is √(3x×15x), which simplifies to √45x². The result is 4x√45x².Multiply 2√3x and 3√60x³: 2x3 is 6, and √3x×√60x³ is √(3x×60x³), which simplifies to √180x⁴. The result is 6√180x⁴.
Finally, combine these products: 4x√45x² + 6√180x⁴.