I'm stuck on this one:
factoring polynomials from algebraic expressions (and it says you can use the substitution method):
3m^2(2p^2+3)over (x^2+y)(2x-y^2)
minus
6m(2p^2+3)over (y^2-x)(2x-y^2)=
Do I find the GCF? I get 3m(m-2) over (x^2+y)(2x-y)(y^2-x) ????
from the top you can factor out 3m(2p^2+3) .
3m(2p^2+3) [m(y^2-x) - 2(x^2+y)] / [(x^2+y)(2x-y^2)(y^2-x)]
I really don't see the point of going further, since none of the terms are alike.
To factor the given expression, you should use the distributive property to factor out the common factor from both terms. Here's how you can do it step by step:
Step 1: Identify the common factor in both terms.
In this case, the common factor is (2p^2 + 3).
Step 2: Factor out the common factor from each term.
First, factor out (2p^2 + 3) from the first term:
3m^2(2p^2 + 3) = 6m^2p^2 + 9m^2
Next, factor out (2p^2 + 3) from the second term:
-6m(2p^2 + 3) = -12mp^2 - 18m
Step 3: Write the factored expression.
Now, you can write the expression with the common factor factored out:
6m^2p^2 + 9m^2 - 12mp^2 - 18m
Step 4: Combine like terms.
To simplify further, combine like terms if possible. In this case, you can combine the terms with the same variables and exponents:
(6m^2p^2 - 12mp^2) + (9m^2 - 18m)
Step 5: Factor out any remaining common factors if possible.
In this case, we can factor out common factors from each part separately:
6mp^2(m - 2) + 9m(m - 2)
Step 6: Simplify further if needed.
Now, you can notice that the two terms have a common factor of (m - 2). Factor that out:
(m - 2)(6mp^2 + 9m)
So, the factored expression is (m - 2)(6mp^2 + 9m).
Note: The GCF (Greatest Common Factor) usually refers to finding the greatest factor that divides multiple terms completely. In this case, we are factoring out a common factor, but it might not necessarily be the GCF.