Algebraic Expressions NCERT Exercise 12.3
Question 7: Simplify these expressions and find their values if `x = 3`, `a = - 1` and `b = - 2`.
(a) `3x – 5 – x + 9`
Answer: `3x – 5 – x + 9`
`= 3 × 3 – 5 – 3 + 9`
`= 9 – 8 + 9 = 18 – 8 = 10`
(b) `2 – 8x + 4x + 4`
Answer: `2 – 8x + 4x + 4`
`= 2 – 8 × 3 + 4 × 3 + 4`
`= 2 – 24 + 12 + 4 ``= 18 – 24 = - 6`
(c) `3a + 5 – 8a + 1`
Answer: `3a + 5 – 8a + 1`
`= 3 × ( - 1) + 5 – 8 × ( - 1) + 1`
`= - 3 + 5 + 8 + 1 ``= - 3 + 14 = 11`
(d) `10 – 3b – 4 – 5b`
Answer: `10 – 3b – 4 – 5b`
`= 10 – 3 × ( - 2) – 4 – 5 ( - 2)`
`= 10 + 6 – 4 + 10 ``= 26 – 4 = 22`
(e) `2a – 2b – 4 – 5 + a`
Answer: `2a – 2b – 4 – 5 + a``= 2(-1) – 2 ( – 2) – 4 – 5 -1``= -2 + 4 – 4 – 5 -1`` = 4-12=-8`
Question 8: If `z = 10`, find the value of `z^3 – 3(z – 10)`
Answer: `z^3 – 3(z – 10)`
`= 10^3 – 3(10 – 10)`
`= 1000 – 3 × 0 = 1000`
Question 9: If `p = - 10`, find the value of `p^2 – 2p – 100`
Answer: `p^2 – 2p – 100`
`= ( - 10)^2 – 2 × ( - 10) – 100`
`= 100 + 20 – 100 = 20`
Question 10: What should be the value of a if the value of `2x^2 + x – a` equals to 5, when `x = 0`?
Answer: `2x^2 + x – a = 5`
Or, `2 × 0^2 + 0 – a = 5`
Or, `- a = 5`
Or, `a = - 5`
Question 11: Simplify the expression and find its value when `a = 6` and `b = - 3`.
`2(a^2 + ab) + 3 – ab`
Answer: `2(a^2 + ab) + 3 – ab`
`= 2[6^2 + 6 × ( - 3)] + 3 – 6 × ( - 3)`
`= 2(36 – 18) + 6 + 18`
`= 2 × 18 + 24 = 36 + 24 = 60`
Exercise 12.4
Question 1: Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.
If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind
Answer: `5 = 5n`, `10 = 10n`, `100 = 100n` Where n = number of segments
Question 2: Use the given algebraic expression to complete the table of number patterns.
Answer:
| S. No. | Expressions | Terms | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1st | 2nd | 3rd | 4th | 5th | 9th | 10th | 50th | 100th | 200th | ||
| (a) | 2n - 1 | 1 | 3 | 5 | 7 | 9 | 17 | 19 | 99 | 199 | 399 |
| (b) | 3n + 2 | 5 | 8 | 11 | 14 | 17 | 29 | 32 | 102 | 302 | 602 |
| (c) | 4n + 1 | 5 | 9 | 13 | 17 | 21 | 37 | 41 | 201 | 401 | 801 |
| (d) | 7n + 20 | 27 | 34 | 41 | 48 | 55 | 83 | 90 | 370 | 720 | 1420 |
| (e) | n2 + 1 | 2 | 5 | 10 | 17 | 26 | 82 | 101 | 2501 | 10,001 | 10,001 |