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Factorize the algebraic expression $36a^2+36a+9$.
Given:
The given algebraic expression is $36a^2+36a+9$.
To do:
We have to factorize the expression $36a^2+36a+9$.
Solution:
Factorizing algebraic expressions:
Factorizing an algebraic expression means 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.
$36a^2+36a+9$ can be written as,
$36a^2+36a+9=(6a)^2+2(6a)(3)+(3)^2$ [Since $36a^2=(6a)^2, 9=(3)^2$ and $36a=2(6a)(3)$]
Here, we can observe that the given expression is of the form $m^2+2mn+n^2$. So, by using the formula $(m+n)^2=m^2+2mn+n^2$, we can factorize the given expression.
Here,
$m=6a$ and $n=3$
Therefore,
$36a^2+36a+9=(6a)^2+2(6a)(3)+(3)^2$
$36a^2+36a+9=(6a+3)^2$
$36a^2+36a+9=(6a+3)(6a+3)$
Hence, the given expression can be factorized as $(6a+3)(6a+3)$.
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