Algebraic Expressions

Exercise 12.3

Question 1: If `m = 2`,find the value of:

  1. `m – 2`

    Answer: `m – 2 = 2 – 2 = 0`
  2. `3m – 5`

    Answer: `3m – 5 = 3 × 2 – 5 = 6 – 5 = 1`
  3. `9 – 5m`

    Answer: `9 – 5m = 9 – 5 × 2 = 9 – 10 = - 1`
  4. `3m^2 – 2m – 7`

    Answer: `3m^2 – 2m – 7`
    `= 3 × 2^2 – 2 × 2 – 7`
    `= 3 × 4 – 4 – 7`
    `= 12 – 4 – 7 = 12 – 11 = 1`
  5. `(5m)/(2) – 4`

    Answer: `(5m)/(2) – 4`
    `= 5 × 2 ÷2 – 4`` = 5 – 4 = 1`

Question 2: If `p = - 2`, find the value of:

(a) 4p + 7

Answer: `4p + 7 = 4 xx ( - 2) + 7`
`= - 8 + 7 = - 1`

(b) `– 3p^2 + 4p + 7`

Answer: `- 3p^2 + 4p + 7`
`= - 3 × (- 2)^2 + 4 × ( - 2) + 7`
`= - 3 × 4 – 8 + 7 = 12 – 8 + 7 = 11`

(c) `– 2p^3 – 3p^2 + 4p + 7`

Answer: `- 2p^3 – 3p^2 + 4p + 7`
`= - 2 × - 2^3 – 3 × (- 2)^2 + 4 × ( - 2) + 7`
`= (- 2) × ( - 8) – 3 × 4 – 8 + 7`
`= 16 – 12 – 8 + 7 = 3`

Question 3: Find the value of the following expressions, when `x = - 1`:/p>

(a) `2x – 7`

Answer: `2x – 7 = 2 xx ( - 1) – 7`
`= - 2 – 7 = - 9`

(b) `– x + 2`

Answer: `- x + 2 = - ( - 1) + 2 = 1 + 2 = 3`

(c) `x^2 + 2x + 1`

Answer: `x^2 + 2x + 1 = - 1^2 + 2 × ( - 1) + 1`
`= 1 – 2 + 1 = 0`

(d) `2x^2 – x – 2`

Answer: `2x^2 – x – 2`
`= 2 × ( - 1)^2 – ( - 1) – 2`
`= 2 + 1 – 2 = 1`


Question 4: If `a = 2`, `b = - 2`, find the value of:

(a) `a^2 + b^2`

Answer: `a^2 + b^2`` = 2^2 + ( - 2)^2`
`= 4 + 4 = 8`

(b) `a^2 + ab + b^2`

Answer: `a^2 + ab + b^2`
`= 2^2 + 2 × ( - 2) + ( - 2)^2`
`= 4 – 4 + 4 = 4`

(c) `a^2 – b^2`

Answer: `a^2 – b^2 = 2^2 – ( - 2)^2`` = 4 – 4 = 0`


Question 5: When `a = 0`, `b = - 1`, find the value of the given expressions:

(a) `2a + 2b`

Answer: `2a + 2b = 0 + 2 xx ( - 1) = - 2`

(b) `2a^2 + b^2 + 1`

Answer: `2a^2 + b^2 + 1`
`= 0 + ( - 1)^2 + 1 = 1 + 1 = 2`

(c) `2a^2b + 2ab^2 + ab`

Answer: `2a^2b + 2ab^2 + ab`
`= 0 + 0 + 0 = 0`

(d) `a^2 + ab + 2`

Answer: `a^2 + ab + 2 = 0 + 0 + 2 = 2`

Question 6: Simplify the expressions and find the value if x is equal to 2.

(a) `x + 7 + 4 (x – 5)`

Answer: `x+ 7 + 4 (x – 5)`
`= 2 + 7 + 4 ( 2 – 5)`
`= 9 + 4 × ( - 3) = 9 – 12 = - 3`

(b) `3(x + 2) + 5x – 7`

Answer: `3(x + 2) + 5x – 7`
`= 3 (2 + 2) + 5 × 2 – 7`
`= 3 × 4 + 10 – 7 = 12 + 3 = 15`

(c) `6x + 5(x – 2)`

Answer: `6x + 5(x – 2)`
`= 6 × 2 + 5 ( 2 – 2)`
`= 12 + 0 = 12`

(d) `4(2x – 1) + 3x + 11`

Answer: `4(2x – 1) + 3x + 11`
`= 4 (2 × 2 – 1) + 3 × 2 + 11`
`= 4 (4 – 1) + 6 + 11`
`= 4 × 3 + 17 = 12 + 17 = 29`



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