Find two binomials whose product is 15,600 and explain how you get it.
To find two binomials whose product is 15,600, we need to break down 15,600 into its prime factors. This will help us identify two numbers whose product equals 15,600.
Let's start by finding the prime factorization of 15,600:
15,600 = 2 × 2 × 2 × 2 × 3 × 5 × 5 × 13
Now, we need to group these prime factors into two separate binomials. Since we need to find two binomials whose product is 15,600, we can group the prime factors in any way that satisfies this condition.
Let's pair the prime factors by grouping the first two, the next two, and so on:
(2 × 2 × 2 × 2 × 3) × (5 × 5 × 13)
Simplifying, we have:
(2^4 × 3) × (5^2 × 13)
Now, we can express these factors as two binomials:
(2^2 × 3) × (5^1 × 13)
(2^2 × 3) and (5^1 × 13) are the two binomials whose product is 15,600. In other words:
(4 × 3)(5 × 13) = 15,600
Therefore, the two binomials whose product is 15,600 are (4 × 3) and (5 × 13).