what is 56+32 distributive property to factor out the greatest common factor.
The Correct Answer and Explanation is:
To apply the distributive property and factor out the greatest common factor (GCF) for the expression 56+3256 + 3256+32, we follow these steps:
Step 1: Identify the GCF
First, we need to find the GCF of the two numbers, 56 and 32.
The factors of 56 are:
- 1, 2, 4, 7, 8, 14, 28, 56.
The factors of 32 are:
- 1, 2, 4, 8, 16, 32.
The greatest common factor (GCF) is the largest number that appears in both lists of factors. In this case, the GCF of 56 and 32 is 8.
Step 2: Apply the distributive property
Now, we use the distributive property to factor out the GCF. The distributive property states that: a+b=c(a+b)a + b = c(a + b)a+b=c(a+b)
where ccc is the GCF. So, we factor out 8 from both terms in the expression 56+3256 + 3256+32: 56+32=8(7+4)56 + 32 = 8(7 + 4)56+32=8(7+4)
Step 3: Verify the result
To verify that the factoring is correct, we can expand the expression 8(7+4)8(7 + 4)8(7+4) back out: 8(7+4)=8×7+8×4=56+328(7 + 4) = 8 \times 7 + 8 \times 4 = 56 + 328(7+4)=8×7+8×4=56+32
This confirms that our factoring is correct.
Final Answer:
The factored form of 56+3256 + 3256+32 is: 56+32=8(7+4)56 + 32 = 8(7 + 4)56+32=8(7+4)
Explanation:
We applied the distributive property by first identifying the greatest common factor (GCF) of 56 and 32, which is 8. By factoring out 8, we simplified the expression to 8(7+4)8(7 + 4)8(7+4), which is equivalent to the original sum. This shows how the distributive property can help factor expressions efficiently by identifying common factors.
