Factor 56p-32q. Write your answer as a product with a whole number greater than 1
The correct answer and explanation is:
To factor the expression 56p−32q56p – 32q, follow these steps:
Step 1: Identify the greatest common factor (GCF)
The terms in the expression are 56p56p and 32q32q. First, we need to find the GCF of 56 and 32. This can be done by finding the factors of both numbers.
- The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
- The factors of 32 are 1, 2, 4, 8, 16, and 32.
The greatest common factor of 56 and 32 is 8.
Step 2: Factor out the GCF
Now, factor out the GCF, which is 8, from both terms in the expression. 56p−32q=8(7p−4q)56p – 32q = 8(7p – 4q)
Step 3: Verify the factorization
To ensure the factorization is correct, distribute the 8 back to the terms inside the parentheses: 8(7p−4q)=8×7p−8×4q=56p−32q8(7p – 4q) = 8 \times 7p – 8 \times 4q = 56p – 32q
This confirms that the factorization is correct.
Final Answer:
56p−32q=8(7p−4q)56p – 32q = 8(7p – 4q)
In conclusion, the expression 56p−32q56p – 32q is factored as the product of 88 and the binomial (7p−4q)(7p – 4q). The GCF was 8, which was factored out, leaving the simplified binomial inside the parentheses.