Question

How do you factor $36{p^4} - 48{p^3} + 16{p^2}$ ?

Answer 1

Hint: For solving this particular question $36{p^4} - 48{p^3} + 16{p^2}$ , Prime factorization: It is the process where the original given number is expressed as the product of prime numbers.
For this we have to calculate the prime factor of the given equation $36{p^4} - 48{p^3} + 16{p^2}$ . Questions similar in nature as that of above can be approached in a similar manner and we can solve it easily.

Complete step by step answer:
We have the following expression,
$36{p^4} - 48{p^3} + 16{p^2}$
Now we know we have to do factorization of $36{p^4} - 48{p^3} + 16{p^2}$ ,
Prime factorization: It is the process where the original given number is expressed as the product of
prime numbers.
Factorization of $36{p^4} - 48{p^3} + 16{p^2}$ :
First of all, take ${p^2}$ common from the above equation, we will get the following expression,
$ \Rightarrow {p^2}(36{p^2} - 48p + 16)$
Now, also take four out of the bracket, we will get the following expression,
$ \Rightarrow 4{p^2}(9{p^2} - 12p + 4)$
Simplify the above expression by splitting the middle term , we will get the following expression,
$
   \Rightarrow 4{p^2}(9{p^2} - 6p - 6p + 4) \\
   \Rightarrow 4{p^2}(3p(3p - 2) - 2(3p - 2)) \\
   \Rightarrow 4{p^2} \times {(3p - 2)^2} \\
 $
Hence we get the final result as given below ,
Factorization of the given expression that is $36{p^4} - 48{p^3} + 16{p^2}$ is given as ,
$36{p^4} - 48{p^3} + 16{p^2} = 4{p^2} \times {(3p - 2)^2}$

Note: Questions similar in nature as that of above can be approached in a similar manner and we can solve it easily. The above question can also be done by simply listing all the possible factors of the given expression by taking common factors out of the bracket and then applying middle term splitting technique. Prime factorization: It is the process where the original given number is expressed as the product of prime numbers.