Simplify the following expressions.

15. 5 (5w-4w)/10

17. 6a X 5b^2/3a^3

20. (4f + 13g) (2w)

Where are your answers?

To simplify these expressions, we can use basic algebraic rules. Let's go through each expression step by step.

15. 5 (5w-4w)/10:
First, we simplify the expression inside the brackets: 5w - 4w = w.
Now we have 5w/10. To simplify further, we divide both the numerator and denominator by their greatest common factor, which is 5. So, we get w/2 as the simplified expression.

17. 6a X 5b^2/3a^3:
To simplify this expression, we multiply the coefficients (6 and 5). So, 6a * 5 = 30a.
Next, we multiply the variables with the same base (a and a^3). a * a^3 = a^(1+3) = a^4.
Finally, we multiply the remaining variable terms: 30a * b^2 = 30ab^2.
Thus, the simplified expression is 30ab^2/3a^3. To simplify it further, we divide both the numerator and denominator by their greatest common factor, which is 3a. So, we get 10b^2/a^2.

20. (4f + 13g) (2w):
To simplify this expression, we need to apply the distributive property, which states that when multiplying a sum or difference by a number, we distribute that number to each term inside the parentheses.
First, we multiply 4f by 2w, which gives us 8fw.
Next, we multiply 13g by 2w, which gives us 26gw.
Thus, the simplified expression is 8fw + 26gw.