Final answer:
To simplify the product 2√(5x³)(-3√(10x²)), you can multiply the coefficients and then multiply the square roots. The simplified product is -30x²√(2x).
Step-by-step explanation:
Coefficients are crucial in algebraic manipulations, and they provide information about the relative size or scale of different terms within an expression. Understanding coefficients is fundamental when simplifying expressions, solving equations, and analyzing the behavior of functions.
To simplify the product 2√(5x³)(-3√(10x²)), we can first multiply the coefficients: 2 * (-3) = -6.
Next, we can multiply the square roots: √(5x³) * √(10x²) = √((5x³)(10x²)) = √(50x5)= √(25x4) * √(2x) = 5x²√(2x).
Therefore, the simplified product is -6 * 5x²√(2x) = -30x²√(2x).