Suppose the given numbers for a mental calculation (see Problem 59) are 10x + y and 10x + z. Notice that these two numbers have the same tens digit. Also assume that y + z = 10, which says that the units digits of the two numbers sum to 10. Algebraically show why the mental calculation described in Problem 59 "works."

Data from Problem 59

Binomial products can be used to do mental calculations. For example, to multiply a pair of two-digit numbers whose tens digits are the same and whose units digits add up to 10, mentally multiply the units digits and then multiply the tens digit of the first number by one more than the tens digit of the second. For example,

Transcribed Image Text:

[*8*9=72] 84 x 8672 24 Laxd. c. 63 X 67 e. 75 4x6 =24- Mentally multiply the given numbers. a. 62 x 68 b. 57 x 53 d. 95