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Sagot :
The factored form of a - b is [tex]\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)[/tex].
What is monomial factorization ?
A monomial is an expression that is the product of constant and non-negative integer powers of x, like [tex]3x^{2}[/tex]..
A monomial is expressed as a product of two or more other monomials when it is factored.
Here,
a = 125
[tex]$b=27 p^{12}$[/tex]
To find: a - b
a - b = 125 - [tex]27 p^{12}$[/tex]
a - b = [tex]5^{3}-\left(3 p^{4}\right)^{3}$[/tex]
We know that,
[tex]$x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$[/tex]
Finding the factored form of a - b using this method:
[tex]$a - b=\left(5-3 p^{4}\right)\left(5^{2}+5\left(3 p^{4}\right)+\left(3 p^{4}\right)^{2}\right)$[/tex]
[tex]$a-b=\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex]
So, factored form of a - b is [tex]$\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex].
Learn more about monomial factorization here:
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