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Factorize the algebraic expression $9a^2-24ab+16b^2$.
Given:
The given algebraic expression is $9a^2-24ab+16b^2$.
To do:
We have to factorize the expression $9a^2-24ab+16b^2$.
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.
$9a^2-24ab+16b^2$ can be written as,
$9a^2-24ab+16b^2=(3a)^2-2(3a)(4b)+(4b)^2$ [Since $9a^2=(3a)^2, 16b^2=(4b)^2$ and $24ab=2(3a)(4b)$]
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,
$m=3a$ and $n=4b$
Therefore,
$9a^2-24ab+16b^2=(3a)^2-2(3a)(4b)+(4b)^2$
$9a^2-24ab+16b^2=(3a-4b)^2$
$9a^2-24ab+16b^2=(3a-4b)(3a-4b)$
Hence, the given expression can be factorized as $(3a-4b)(3a-4b)$.
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