Factor completely.
36a^3b^2+66a^2b^3-210ab^4
Is this correct?
6ab^2(6a^2+11ab-35b^2)
Yes, it is correct as far as it goes. But
(6a^2+11ab-35b^2)
is also factorable into
(3a - _b)(2a + _b). See if you can figure out the missing numbers
So would it be 6ab^2(3a-5b)(2a+7b)?
To factor the given expression completely, you can follow these steps:
Step 1: Find the Greatest Common Factor (GCF) of all the terms in the expression. In this case, the GCF is 6ab^2 since it is the largest value that divides all the coefficients and variables.
Step 2: Divide each term in the expression by the GCF (6ab^2). This will distribute the GCF outside a set of parentheses.
Dividing each term by the GCF yields:
(36a^3b^2)/(6ab^2) + (66a^2b^3)/(6ab^2) - (210ab^4)/(6ab^2)
Simplifying, we get:
6a + 11ab - 35b^2
Step 3: Now, you need to factor the trinomial expression (6a + 11ab - 35b^2) further. However, it cannot be factored easily by finding common factors or perfect square terms. So, let's use the AC method or trial and error:
The AC method involves finding two numbers that multiply to give the product of the coefficient of the squared term (6) and the constant term (-35), which is -210. These two numbers must add up to the coefficient of the linear term (11).
The numbers in this case are -14 and 15, since (-14) * 15 = -210 and (-14) + 15 = 1.
We can rewrite the expression as:
6a + 14ab - 3ab - 35b^2
Next, we group the terms:
(6a + 14ab) - (3ab + 35b^2)
Now, factor out the GCF from each group:
2a(3 + 7b) - b(3a + 35b)
Thus, the completely factored expression is:
6ab^2(2a + 7b) - b(3a + 35b)
So, your answer is incorrect. The correct factored form is:
6ab^2(2a + 7b) - b(3a + 35b)