Now let’s try to find the answer for the squares of these numbers:
18, 27, and 38
Example 1:
1- 18 = (20-2) and 18²= (20 – 2)²
The reason we want to change it to 20 – 2 is so that it is easier to find the square of 20 than the square of 18. The square of 20 = 400.
Let’s apply the following formula (a - b)² = a² - 2ab + b². In this example (a = 20) and (b = 2)
2- a² = 20² = 400
3- 2ab = 2(20 × 2) = 2(40) = 80. Which is double the product of (a × b)
4- b² = 2² = 2 × 2 = 4
Now let’s add all together using the Square of Binomial formula.
a² - 2ab + b² = 400 – 80 + 4 the numbers we got from steps 2,3 and 4.
(400 – 80) + 4 = 320 + 4 = 324
So 18 × 18 = 324
Let’s do another one.
Example 2:
1- 27 = (30-3) and 27²= (30 – 3)²
The reason we want to change it to 30 – 3 is so that it is easier to find the square of 30 than the square of 27. The square of 30 = 900
Let’s apply the following formula (a - b)² = a² - 2ab + b². In this example (a = 30) and (b = 3)
2- a² = 30² = 900
3- 2ab = 2(30 × 3) = 2(90) =180. Which is double the product of (a × b)
4- b² = 2² = 3 × 3 = 9
Now let’s add all together using the Square of Binomial formula.
a² - 2ab + b² = 900 – 180 + 9 the numbers we got from steps 2,3 and 4.
(900 – 180) + 9 = 720 + 9 = 729
So 27 × 27 = 729
For your own practice, try repeating the same process with the number 38. If it would help, try copying and pasting one of the examples and just replace the numbers with the new numbers that correspond to the number 38. You would use (40 - 2) to represent the number 38 in the formula. Since 4 × 4 = 16, 40 × 40 will equal to 1600.
Once you do several examples, you will start finding that it is much easier than you think. The more you practice, the better you will get at it. After you’ve done a few examples, try doing it mentally to see how fast you can come up with the answer.
In the next lesson we will do examples using (a + b)² = a² + 2ab + b². This one should be a little easier since it is all addition, no subtraction involved. Lesson 2
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