How do you multiply algebraic expression such as.....
(5x^3)(4xy^2)
5 * x^3 * 4 * x * y^2
20 x^4 y^2
(5*x*x*x)(4*x*y*y)
To multiply algebraic expressions like (5x^3)(4xy^2), you need to apply the distributive property and combine like terms. Here's how you can do it step by step:
Step 1: Multiply the coefficients (numbers in front of the variables): 5 * 4 = 20.
Step 2: Multiply the variables with the same base by adding their exponents. In this case, we have 'x' raised to the power of 3 and 'x' raised to the power of 1, and 'y' raised to the power of 2 and 'y' raised to the power of 1.
For 'x': 3 + 1 = 4
For 'y': 2 + 1 = 3
So, you have x^4 and y^3.
Step 3: Put the multiplied coefficients (20) together with the multiplied variables (x^4 and y^3) to get the final answer.
Final Answer: 20x^4y^3
Therefore, (5x^3)(4xy^2) = 20x^4y^3.