Number Operations and Properties

(7k + 2) (12p + 5) = 84pk + 35k + 24p + 10                        (Using Foil)

(p - 5) (7p + 2) = 7p² + 2p - 35p - 10 (Using Foil) = 7p² - 33p - 10

(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

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.

In octal number system, we have 8 digits from 0 to 7 ony. Hence, 578 is not an octal number.

1101 + 101 = 1202 in any number system where digits upto 2 are present. This is so in all the number systems with base 3 or more.

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.