Now let’s try to find the answer for the squares of these numbers:
24, 33, and 42
Example 1:
1- 24 = (20+4) and 24²= (20 + 4)²
The reason we want to change it to 20 + 4 is so that it is easier to find the square of 20 than the square of 24. The square of 20 = 400.
Let’s apply the following formula (a + b)² = a² + 2ab + b². In this example
a = 20 and
b = 4
2- a² = 20² = 20 × 20 = 400
3- 2ab = 2(20 × 4) = 2(80) = 160. Which is double the product of (a × b)
4- b² = 4² = 4 × 4 = 16
Now let’s add all together using the Square of Binomial formula.
a² + 2ab + b² = 400 + 160 + 16 the numbers we got from steps 2, 3 and 4.
(400 + 160) + 16 = 560 + 16 = 576
So 24 × 24 = 576
Let’s do another one.
Example 2:
1- 33 = (30 + 3) and 33²= (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 33. 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 = 30 × 30= 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 = 1080 + 9 = 1089
So 33² = 33 × 33 = 1089
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 42. 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. You can try applying this method to the numbers: 22, 23, and 24. However, for the numbers 26, 27, and 28, it would be easier to try the steps in lesson 1.
