Factor 72p+81.

Question

Write your answer as a product with a whole number greater than 1.

Answer 1

To factor the expression \( 72p + 81 \), we can start by finding the greatest common factor (GCF) of the coefficients 72 and 81.

1. Find the GCF:

   • The prime factorization of \( 72 \) is \( 2^3 \times 3^2 \).
   • The prime factorization of \( 81 \) is \( 3^4 \).
   • The common factor is determined by the lowest powers of the common prime factors.
   • The common prime factor is \( 3 \), and the lowest power is \( 3^2 \), which is \( 9 \).

2. Factor out the GCF:

   • Now we factor \( 9 \) out of the expression: \[ 72p + 81 = 9(8p + 9) \]

Thus, the factored form of \( 72p + 81 \) is \( 9(8p + 9) \).

The answer is \( 9(8p + 9) \).