How do i factorise
1)6a^2b^3+12a^4b
2)2m^2+9m-5
1. 6a^2*b (b^2 + a^2)
2. (2m -1)(m + 5)
To factorize the given expressions, we need to find the common factors for each term and then factor them out.
1) 6a^2b^3 + 12a^4b:
First, we can see that both terms have a common factor of 6ab. Factoring this out, we get:
6ab(a^2b^2 + 2a^3)
Now, we can further factor the expression inside the parenthesis by taking out the common factor of a^2:
6ab(a^2b^2 + 2a^3) = 6ab(a^2(b^2) + 2a(b))
So, the fully factored form of 6a^2b^3 + 12a^4b is 6ab(a^2(b^2) + 2a(b))
2) 2m^2 + 9m - 5:
To factorize this quadratic expression, we need to find two numbers that multiply to give -10 (the product of the coefficient 2 and -5) and add up to 9 (the coefficient of the middle term).
The numbers that satisfy these conditions are 10 and -1. Rewriting the middle term, we have:
2m^2 + 10m - m - 5
Now, we group the terms and factor by grouping:
(2m^2 + 10m) + (-m - 5)
2m(m + 5) - 1(m + 5)
We can see that there is a common factor of (m + 5). Factoring it out, we get:
(m + 5)(2m - 1)
So, the fully factored form of 2m^2 + 9m - 5 is (m + 5)(2m - 1)