Find the shortcut.
Solve these problems. Then find and explain a shortcut method for finding the answer.
52(Squared) - 42 (squared) =
82 (Squared) - 72 (Squared) =
122 (Squared) - 112 (Squared) =
312 (Squared) - 302 (Squared) =
892 (Squared) - 882 )(Squared =
I know now Add them together without squaring.
To solve these problems, you need to calculate the difference between two squares. The general formula for finding the difference between two squares is:
(a^2 - b^2) = (a - b)(a + b)
Now let's apply this formula to the given problems.
For the first problem:
52^2 - 42^2 = (52 - 42)(52 + 42) = 10 * 94 = 940
Shortcut Method:
To find the difference between two squares, square the sum of the two numbers and then subtract the product of the two numbers. Let's use this shortcut method for the remaining problems.
For the second problem:
82^2 - 72^2 = (82 - 72)(82 + 72) = 10 * 154 = 1540
For the third problem:
122^2 - 112^2 = (122 - 112)(122 + 112) = 10 * 234 = 2340
For the fourth problem:
312^2 - 302^2 = (312 - 302)(312 + 302) = 10 * 614 = 6140
For the fifth problem:
892^2 - 882^2 = (892 - 882)(892 + 882) = 10 * 1774 = 17740
So, the shortcut method to find the answers is to subtract the squares of the two numbers multiplied by 10.