Question

A and b are monomials where a = 125 and b = 27p12. what is the factored form of a – b?

Answer 1

The factored form of a - b is $\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$.

What is monomial factorization ?

A monomial is an expression that is the product of constant and non-negative integer powers of x, like $3x^{2}$..

A monomial is expressed as a product of two or more other monomials when it is factored.

Here,

a = 125

$b=27 p^{12}$

To find: a - b

a - b = 125 - $27 p^{12}$

a - b =  $5^{3}-\left(3 p^{4}\right)^{3}$

We know that,

$x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$

Finding the factored form of a - b using this method:

$a - b=\left(5-3 p^{4}\right)\left(5^{2}+5\left(3 p^{4}\right)+\left(3 p^{4}\right)^{2}\right)$

$a-b=\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$

So, factored form of a - b is $\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$.

Learn more about monomial factorization here:

brainly.com/question/26278710

#SPJ4