Write 28 + 24 as a product of two factors using the GCF and the distributive property. 28 + 24 = ? (? + ? )
The Correct Answer and Explanation is:
We want to express 28+2428 + 2428+24 as a product of two factors using the greatest common factor (GCF) and the distributive property.
Step 1: Find the GCF of 28 and 24.
The first step is to identify the greatest common factor (GCF) of 28 and 24. The factors of 28 are:
- 1, 2, 4, 7, 14, 28.
The factors of 24 are:
- 1, 2, 3, 4, 6, 8, 12, 24.
The GCF of 28 and 24 is 4, as it is the largest number that divides both 28 and 24.
Step 2: Factor out the GCF.
Now that we know the GCF is 4, we can factor 4 out of both terms in the expression 28+2428 + 2428+24.28+24=4(7+6)28 + 24 = 4(7 + 6)28+24=4(7+6)
Step 3: Distributive Property.
The distributive property tells us that a(b+c)=ab+aca(b + c) = ab + aca(b+c)=ab+ac. Here, we’ve factored out the GCF, so we can check:4(7+6)=4×7+4×6=28+244(7 + 6) = 4 \times 7 + 4 \times 6 = 28 + 244(7+6)=4×7+4×6=28+24
Thus, the expression 28+2428 + 2428+24 as a product of two factors is:28+24=4(7+6)28 + 24 = 4(7 + 6)28+24=4(7+6)
Final Answer:
28+24=4(7+6)28 + 24 = 4(7 + 6)28+24=4(7+6)
Explanation:
By using the distributive property and the GCF, we rewrote the sum 28+2428 + 2428+24 as a product of the GCF, 4, and the sum of the remaining factors, 7 and 6. This technique is helpful in simplifying expressions and is widely used in algebra to factor polynomials or combine terms effectively.
