Respuesta :
The correct option is (A). The factored form of a-b is (5-3p⁴)(25+15p⁴+9p⁸).
Given that A and B are monomials where a = 125 and b = 27p¹².
Monomial expressions include only one non-zero term. Numbers, variables, or multiples of numbers and variables are all examples of monomials.
Firstly, substitute a=125 and b = 27p¹² into a-b, we get
a-b=125-27p¹² ......(1)
As we know, 125=(5)³, 27p¹²=(3p⁴)
So, equation (1) can be rewritten as
a-b=(5)³-(3p⁴)
Now, apply a³-b³=(a-b)(a²+ab+b²).
a³-b³=(5-3p⁴)(5²+5(3p⁴)+(3p⁴)²)
Further, Simplify using exponent rule with the same exponent (ab)ⁿ=aⁿbⁿ.
a³-b³=(5-3p⁴)(5²+5×3p⁴+3²×(p⁴)²)
Furthermore, calculate the power, we get
a³-b³=(5-3p⁴)(5²+5×3p⁴+9(p⁴)²)
Then, Simplify using exponent power rule (aˣ)ⁿ=aˣⁿ, we get
a³-b³=(5-3p⁴)(5²+5×3p⁴+9p⁸)
Now, multiply the monomials, we get
a³-b³=(5-3p⁴)(5²+15p⁴+9p⁸)
Further, calculate the power, we get
a³-b³=(5-3p⁴)(25+15p⁴+9p⁸)
Finally, reorder the expressions, we get
a³-b³=(5-3p⁴)(9p⁸+15p⁴+25)
Hence, the factored form of a-b where a and b monomials and a = 125 and b = 27p¹² is (5-3p⁴)(9p⁸+15p⁴+25).
Learn more about monomials from here brainly.com/question/936140
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