How do I solve a problem like this:
p^3m^2/7 + p^2m^3/21 - p^4m/14
Can you please help?
common factor: p^2 m/7
mp^2/7 ( pm+m^2 /2 + p^2/2)
now, consider the ( ) factor out 1/2
1/2 (p^2+2pm+m^2)=1/2 (P+m)^2
so, anwer:
mp^2/14 (p+m)^2
check all that.
To solve the given expression, we can simplify it by combining the terms with the same variables and then perform the arithmetic operations.
The given expression is:
p^3m^2/7 + p^2m^3/21 - p^4m/14
Step 1: Common denominator
To combine the terms with different denominators, we need to find the least common denominator (LCD) of 7, 21, and 14, which is 42.
Step 2: Rewrite the terms with the common denominator
Now, let's rewrite each term with the common denominator and simplify:
(p^3m^2/7) * (6/6)
= (6p^3m^2/42)
(p^2m^3/21) * (2/2)
= (2p^2m^3/42)
(- p^4m/14) * (3/3)
= (-3p^4m/42)
Step 3: Combine the terms
Now, we can combine the simplified terms:
(6p^3m^2/42) + (2p^2m^3/42) - (3p^4m/42)
Step 4: Add or subtract the coefficients
Since the terms have the same denominator (42), we can add or subtract their coefficients:
(6p^3m^2 + 2p^2m^3 - 3p^4m)/42
Therefore, the simplified form of the given expression is:
(6p^3m^2 + 2p^2m^3 - 3p^4m)/42