8. CBQ - Describe and verify the pattern

Question:

4 m.

During a mathematics lesson on pattern investigation, Teju’s teacher wrote the following equation on the board and asked the students to explore the relationship among the numbers:

12 \times 12 - 6 \times 6 = 18 \times 6

Based on this information answer the following.

1. Check if the given equation is true. If yes, what is the answer you get on solving both sides of the equation?

2. Which among the following best describes the product 18 $\times$ 6 with respect to the numbers 12 and 6?

$18 \times 6 = (12 - 6) \times (12 + 6)$
$18 \times 6 = (6 + 6) \times (12 - 6)$
$18 \times 6 = (12 + 6) \times (12 - 6)$
$18 \times 6 = (12 - 6) \times (12 + 12)$

3. Is the relation true if the numbers 12 and 6 are negative. If yes, which among the following is the correct reason?

The square of a negative number is less than zero
Squaring a negative number does not change its sign
Square of a negative number always results in a positive number
The square of a negative number is always negative.

4. Which among the following pattern best describes the equation

12 \times 12 - 6 \times 6 = 18 \times 6

$a^2 - b^2 = (a+b)^2 \times (a-b)^2$
$a^2 - b^2 = (a+b) \times b$
$a^2 - b^2 = (a+b) \times (a-b)$
$a^2 - b^2 = a \times b$

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