Final answer:
To simplify the expression, combine like terms and simplify radicals. The final simplified expression is 9√2x^3y³.
Step-by-step explanation:
To simplify the expression, we need to combine like terms under the same radicals. In this case, both terms have the same radical, so we can add the coefficients (numbers in front of the radicals) and keep the variables and exponents the same. The expression 3√32x^3y³ + √50x^3y³ simplifies to (√32 + √50)x^3y³.
Next, we can simplify the radicals by factoring out perfect squares. The square root of 32 can be expressed as √(16 * 2), which simplifies to 4√2. Similarly, the square root of 50 can be expressed as √(25 * 2), which simplifies to 5√2.
Substituting these simplified radicals back into the expression, we get (4√2 + 5√2)x^3y³. The coefficients (4 and 5) can be added, giving us 9√2x^3y³ as the final simplified expression.