Factor 20b + 36c.
Write your answer as a product
The correct answer and explanation is:
To factor the expression 20b+36c20b + 36c, follow these steps:
Step 1: Identify the greatest common factor (GCF)
First, look for the greatest common factor of the two terms 20b20b and 36c36c. To do this, we need to consider the numerical coefficients (20 and 36) and the variables involved.
- The factors of 20 are 1, 2, 4, 5, 10, and 20.
- The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The greatest common factor of 20 and 36 is 4, as it is the largest number that divides both 20 and 36 evenly.
Next, look at the variables:
- 20b20b has the variable bb, and 36c36c has the variable cc. There is no common variable factor between bb and cc, so the variable part of the GCF is just 1.
Thus, the GCF of the expression 20b+36c20b + 36c is 4.
Step 2: Factor out the GCF
Now, factor out the GCF (which is 4) from the original expression: 20b+36c=4(5b+9c)20b + 36c = 4(5b + 9c)
Step 3: Verify the factorization
To check if the factorization is correct, distribute the 4 back into the terms inside the parentheses: 4(5b+9c)=4×5b+4×9c=20b+36c4(5b + 9c) = 4 \times 5b + 4 \times 9c = 20b + 36c
Since this matches the original expression, the factorization is correct.
Final Answer:
20b+36c=4(5b+9c)20b + 36c = 4(5b + 9c)
This is the factored form of the given expression, and it is written as a product of 4 and 5b+9c5b + 9c.