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Factorize the expression $ab(x^2+1)+x(a^2+b^2)$.
The given expression is $ab(x^2+1)+x(a^2+b^2)$.
We have to factorize the expression $ab(x^2+1)+x(a^2+b^2)$.
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.
Here, we can factorize the expression $ab(x^2+1)+x(a^2+b^2)$ by grouping similar terms and taking out the common factors.
$ab(x^2+1)+x(a^2+b^2)$ can be written as,
The terms in the given expression are $abx^2, ab, a^2x$ and $b^2x$.
We can group the given terms as $abx^2, a^2x$ and $ab, b^2x$.
Therefore, by taking $ax$ as common in $abx^2, a^2x$ and $b$ as common in $ab, b^2x$, we get,
Now, taking $(a+bx)$ common, we get,
Hence, the given expression can be factorized as $(ax+b)(a+bx)$.
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