Factorise:-
25a^2-35a+12
(5a-3)(5a-4)
To factorize the expression 25a^2 - 35a + 12, we are looking for two binomial factors that, when multiplied, will result in this expression.
Step 1: Multiply the coefficient of the quadratic term (25) with the constant term (12). The result is 300.
Step 2: Find two numbers that can be added to get the coefficient of the linear term (-35) and multiplied to get the result from Step 1 (300).
In this case, the two numbers are -20 and -15. When added, -20 + (-15) equals -35, and when multiplied, (-20) * (-15) equals 300.
Step 3: Rewrite the middle term (-35a) using the two numbers found in Step 2. Replace -35a with -20a - 15a.
Now the expression becomes:
25a^2 - 20a - 15a + 12
Step 4: Group the terms in pairs and factor them separately.
(25a^2 - 20a) + (-15a + 12)
Step 5: Factor out the greatest common factor from each pair.
5a(5a - 4) - 3(5a - 4)
Step 6: Now we can see that we have two terms that are the same, (5a - 4). Factor them out.
(5a - 4)(5a - 3)
Therefore, the factorization of 25a^2 - 35a + 12 is (5a - 4)(5a - 3).