Question

What is the simplified product of 2√(8x³) and (3√(10⁴) - x√(5x²))? Assume x ≥ 0.

Answer 1

The simplified product of 2√(8x³) and (3√(10⁴) - x√(5x²)) is 120x²√(2x) - 4x²√(10x³).

Step-by-step explanation:

To find the simplified product of 2√(8x³) and (3√(10⁴) - x√(5x²)), we first simplify each term individually and then multiply them together.

1. First, simplify 2√(8x³) = 2√(4(x²) * 2x).
2. Since 4 is a perfect square, we can simplify further to 2 * 2√(x²) * √(2x) = 4x√(2x).
3. Next, simplify (3√(10⁴) - x√(5x²)) = 3√(10⁴) - x√(5(x²)).
4. Since 10⁴ and 5 are both perfect squares, we can simplify further to 3 * 10 * √(x²) - x * √(5) * √(x²) = 30x - x√(5x²).
5. Finally, multiply the two simplified terms together: 4x√(2x) * (30x - x√(5x²)) = 120x²√(2x) - 4x²√(10x³).

Therefore, the simplified product of 2√(8x³) and (3√(10⁴) - x√(5x²)) is 120x²√(2x) - 4x²√(10x³).