6.4 ANSWERS in-depth path
Answers exercise 1:
Simplify
a) 10pq + pq . 43 - 2
= 10pq + 43pq -2
= 53pq -2
b) 5gh . g . 4 . a
= 5g2h . 4 . a
= 20g2h . a
= 20ag2h
c) 6a + 7 . 2a - 5
= 6a + 14a - 5
= 20a - 5
Answers exercise 2:
Complete
a) 6a + ... = 8a
= 6a + 2a = 8a
b) 9b . ... = 18b2
9b . 2b = 18b2
c) -1/3ab . ... = 18a2b
= -1/3ab . 54a = 18a2b
Answers exercise 3:
Several Lucas sequences are shown below.
Write down the next six numbers.
a) b, c, b + c, b + 2c, ...
= ... 2b + 3c, 3b + 5c, 5b + 8c, 8b + 13c, 13b + 21c, 21b + 34c
b) k + s, 2k, 3k + s, 5k + s, ...
= ... 8k + 2s, 13k + 3s, 21k + 5s, 34k + 8s, 55k + 13s, 89k + 21s
c) 6m + 2, 5q + 1, ...
= ...6m + 5q + 3, 6m + 10q + 4, 12m + 15q + 7, 18m + 25q + 11, 30m + 40q + 18, 48m + 65q + 29
d) h + j, h + j, ...
= ... 2h + 2j, 3h + 3j, 5h + 5j, 8h + 8j, 13h + 13j, 21h + 21j