Question
Which expression shows a way to factor 63+81?
Which expression shows a way to factor 63+81?
Which expression shows a way to factor 63+81?
Answers
Answered by
GPT-4o mini
To factor the expression \(63 + 81\), you can start by finding the greatest common factor (GCF) of the two numbers.
1. First, find the GCF of 63 and 81:
- The prime factorization of 63 is \(3^2 \times 7\).
- The prime factorization of 81 is \(3^4\).
The GCF is the product of the lowest powers of the common prime factors:
- The only common prime factor is 3.
- The lowest power of 3 present in both factorizations is \(3^2\) (from 63).
Thus, the GCF of 63 and 81 is \(9\).
2. Now, we can factor out the GCF:
\[
63 + 81 = 9 \cdot 7 + 9 \cdot 9 = 9(7 + 9)
\]
So, the expression that shows how to factor \(63 + 81\) is:
\[
9(7 + 9)
\]
You could also simplify \(7 + 9\) to get \(9 \cdot 16\), but the factored form is \(9(7 + 9)\).
1. First, find the GCF of 63 and 81:
- The prime factorization of 63 is \(3^2 \times 7\).
- The prime factorization of 81 is \(3^4\).
The GCF is the product of the lowest powers of the common prime factors:
- The only common prime factor is 3.
- The lowest power of 3 present in both factorizations is \(3^2\) (from 63).
Thus, the GCF of 63 and 81 is \(9\).
2. Now, we can factor out the GCF:
\[
63 + 81 = 9 \cdot 7 + 9 \cdot 9 = 9(7 + 9)
\]
So, the expression that shows how to factor \(63 + 81\) is:
\[
9(7 + 9)
\]
You could also simplify \(7 + 9\) to get \(9 \cdot 16\), but the factored form is \(9(7 + 9)\).