Number Operations and Properties

(8p - 2) (6p + 2) = 48p² + 16p - 12p - 4 (Using Foil) = 48p² + 4p - 4

2(7m + 10) (7m - 10) = 2(49m² - 70m + 70m - 100) (Using Foil) = 2(49m² - 100) = 98m² - 200

(4m + 8) (4m - 8) = 16m² - 32m + 32m - 64 (Using Foil) = 16m² - 64

(7m + 8) (8m + 6) = 56m² + 42m + 64m + 48                     (Using Foil) = 56m² + 106m + 48

From 12 to 24, there are 7 even numbers (12, 14, 16, 18, 20, 22, 24).

3k - 21 = 6k - 42 Or 3k = 21 Or k = 7 Now, 2z + 2 = k Or 2z + 2 = 7 Or 2z = 5 Or z = 2.5

Yes, the size of long double is 12.

The series is nⁿ - n. Putting n = 4, we get 252.

This is the right answer. As 35 hundred is equal to 3500. So if we subtract 3500 from 3500 we will get 0.

3500 - 3500 = 0

8 x 8= 64

This is a right answer. To get the number of tens, we  will subtract  690 from 1000 and we will get 310. Now  310 has 31 tens. So this is the right answer.

According to the English alphabet, the code of the word BUT is the sum of backward positions of each letter. As, BUT = 25 + 6 + 7 => 38 Similarly, YET = 2 + 22 + 7 => 31 This is the correct answer.

According to the English alphabet, the code of CASK is the sum of one more than the positions of each letter. As, CASK = (3 + 1) + (1 + 1) + (19 + 1) + (11 + 1) => 38 Similarly, CAR = (3 + 1) + (1 + 1) + (18 + 1) => 25 This is the correct answer.

In the metric system and scientific notation, 'mega' is the SI prefix for 10^6 or one million (1,000,000). Common examples: megabyte (MB) = 1 million bytes, megahertz (MHz) = 1 million hertz. Kilo is 10^3, giga is 10^9, and tera is 10^12. This is a standard SI prefix convention used in science and engineering.

Given,x = 107 x 15 = 1605 Also, y = 115 x 15 = 1725 Therefore, x + y = 1725 + 1605 = 3330. Therefore, (x + y)/10 = 333 Rounded off to the nearest tens, it becomes 330.