Factor each expression by grouping. Can you please show me the steps on how you get your answer so I know how to do the problem thank you.
9p^2+mn^2+9m+p^2n^2
To factor the expression 9p^2 + mn^2 + 9m + p^2n^2 by grouping, follow these steps:
Step 1: Group the terms in pairs:
(9p^2 + p^2n^2) + (mn^2 + 9m)
Step 2: Find the greatest common factor (GCF) of each pair:
For the first pair, the GCF is p^2.
For the second pair, the GCF is m.
Step 3: Factor out the GCF from each pair:
p^2(9 + n^2) + m(n^2 + 9)
Step 4: Notice that the expressions inside the parentheses are now the same:
p^2(9 + n^2) + m(9 + n^2)
Step 5: Factor out the common binomial factor (9 + n^2):
(9 + n^2)(p^2 + m)
The final factored form of the expression 9p^2 + mn^2 + 9m + p^2n^2 is (9 + n^2)(p^2 + m).