I need help in finding the factorization of -60m2 + 15n2...
also the factorization of 6x2 - 2x - 20
Please help
To find the factorization of -60m^2 + 15n^2, we need to look for common factors in each term. In this case, we notice that -60m^2 and 15n^2 both have a common factor of 15. Also, we can factor out the highest power of the variable from each term, which is m^2 from -60m^2 and n^2 from 15n^2.
Taking out the common factor 15, we have:
-60m^2 + 15n^2 = 15(-4m^2 + n^2)
Now let's focus on the expression -4m^2 + n^2. This is a difference of squares, which can be further factorized as (2m + n)(2m - n).
Therefore, the factorization of -60m^2 + 15n^2 is:
-60m^2 + 15n^2 = 15(2m + n)(2m - n).
Moving on to the second expression 6x^2 - 2x - 20, we need to look for common factors and use factoring techniques. In this case, we don't have a common factor among all three terms, so we will start with factoring by grouping.
First, let's group the terms:
(6x^2 - 2x) - 20
In the first group, we can factor out the common factor of 2x:
2x(3x - 1) - 20
Now, let's factor out the common factor of 2 from the entire expression:
2(x(3x - 1) - 10)
Thus, the factorization of 6x^2 - 2x - 20 is:
6x^2 - 2x - 20 = 2(x(3x - 1) - 10)
To verify the factorization, you can expand the factors to see if you get back the original expression.