Final answer:
We simplified the expression by factoring out perfect squares from the radicals, combining like terms, and simplifying the coefficients, resulting in the final simplified product: 12√20 x⁵⁹ - 4√10x².
Step-by-step explanation:
The student has asked to simplify the following algebraic expression:
2√8x³(3√ 10x⁴-x √5x²)
First, we can simplify the radicals and factor out any perfect squares:
Now, let's apply these simplifications to the expression:
2 ⋅ 2√2 ⋅ x²⋅½ (3√10x⁴ - x ⋅ √5 ⋅ x)
Multiplying through the parentheses gives us:
4√2x²⋅½ ⋅ 3√10x⁴ - 4√2x²⋅½ ⋅ x√5x
Rewriting the expressions in terms of exponents:
12√2√10 x³∙¾ - 4√2√5 x³∙½⋅½
Finally, simplifying the coefficients and combining like terms:
12√20 x⁵⁹ - 4√10x²
Which is the simplified product.