To find the product of the expression x2 * 2x * 3 * 4 * x2 * 5x * 6, you should follow a step-by-step approach to combine the terms properly. Below is a detailed breakdown of the process.
1. **Identify and group the like terms:**
In the expression, we have terms involving ‘x’ and constant numbers. The terms with ‘x’ can be grouped together while the constants can be multiplied together separately.
2. **Combine the ‘x’ terms:**
The ‘x’ terms are x2, 2x, x2, and 5x. To combine them, we need to add the exponents of ‘x’. So, we have:
– x2 (from the first part)
– 2x can be considered as 2 * x1
– Another x2 from the middle of the expression
– 5x can be written as 5 * x1
Thus, the total exponent of ‘x’ becomes:
2 + 1 + 2 + 1 = 6, giving us x6.
3. **Multiply the constant numbers:**
Now, we can multiply all the constants in the expression: 2, 3, 4, 5, and 6.
– First, multiply 2 and 3 to get 6.
– Next, multiply 6 by 4 to get 24.
– Then multiply 24 by 5 to get 120.
– Finally, multiply 120 by 6 to get 720.
4. **Put it all together:**
Finally, combine the constants we found with the ‘x’ term we derived. Therefore, the full product of the original expression is:
720 * x6.
In conclusion, the product of the expression x2 * 2x * 3 * 4 * x2 * 5x * 6 results in 720x6.