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Factorize the expression $3a^5-48a^3$.
Given:
The given algebraic expression is $3a^5-48a^3$.
To do:
We have to factorize the expression $3a^5-48a^3$.
Solution:
Factorizing algebraic expressions:
Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution.
An algebraic expression is factored completely when it is written as a product of prime factors.
$3a^5-48a^3$ can be written as,
$3a^5-48a^3=3a^3(a^2-16)$ (Taking $3a^3$ common from both the terms)
$3a^5-48a^3=3a^3(a^2-4^2)$ [Since $16=4^2$]
Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression.
Therefore,
$3a^5-48a^3=3a^3(a^2-4^2)$
$3a^5-48a^3=3a^3[(a+4)(a-4)]$
$3a^5-48a^3=3a^3(a+4)(a-4)$
Hence, the given expression can be factorized as $3a^3(a+4)(a-4)$.
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