Question

Use the difference of two squares to find the product of 22 and 18. Enter the correct number in each box. ( + )( − ) = ( )2 − ( )2 = 396

Answer 1

Explanation:

= (20 + 2) × (20 - 2)

= 22 × 18

= a^2 - b^2 = 396

= (a + b) × (a - b) = 396

From the above, a = 20 and b = 2.

Therefore,

(20^2) - (2^2) = 396.

Answer 2

(20+2) (20-2) = 20² - 2²

20² - 2² = 396

Explanation:

from the rule of the difference of two square which states thate

(a + b)(a − b) = a² − b²

therefore, 22 can also be written as (20 + 2),

while 18 can be written as (20 -2)

therefore by the rule of the difference of two square the product of both expression will give

(20+2) (20-2) = 20² - 2² = 400 - 4 = 396