Final answer:
Using the special product pattern, we can calculate the product of 16 and 24 by expressing them as 20 - 4 and 20 + 4 and using the pattern (a - b)(a + b) = a^2 - b^2 to find that 16 * 24 equals 384.
Step-by-step explanation:
To use special product patterns to find the product of 16 * 24, we can employ the method of finding areas of rectangles by adding and subtracting suitable numbers in a method similar to completing the square. Here's a step-by-step explanation:
- First, express each number as the sum and difference of numbers that have a common product: 16 = 20 - 4 and 24 = 20 + 4.
- Imagine these as the lengths and widths of rectangles where one set of sides is 20 units long and the other differs by 4 units, one being 4 units more and the other being 4 units less.
- Now, think of this as an application of the special product pattern (a + b)(a - b) = a^2 - b^2.
- Calculate the product: (20 - 4)(20 + 4) which equals 20^2 - 4^2 = 400 - 16 = 384.
Hence, using special product patterns, 16 * 24 equals 384.