Class 8 Maths

Algebraic Expressions

Exercise 9.1

Question 1: Identify the terms, their coefficients for each of the following expressions.

(i) `5xyz^2 – 3zy`

Answer: Term: `xyz^2` -- Coefficient `= 5`
Term: `zy` -- Coefficient `= 3`

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

Answer: Term: `x` -- Coefficient `= 1` and Term: `x^2` -- Coefficient = 1

(iii) `4x^2y^2 – 4x^2y^2z^2+ z^2`

Answer: 4 is the coefficient for `x^2y^2z^2`
1 is the term for `z^2`

(iv) `3 – pq + qr – rp`

Answer: For each term the coefficient is 1

(v) `x/2-y/2=xy`

Answer: `1/2` is the coefficient for x and y and for xy it is 1

(vi) `0.3a – 0.6ab + 0.5b`

Answer: 0.3 is the coefficient for a, for b there are two coefficients 0.6 and 0.5

Question 2: Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?

Answer:

  1. `x + y`: Binomial
  2. 1000: Monomial
  3. `x + x^2 + x^3 + x^4`: Polynomial
  4. `7 + y + 5x`: Binomial
  5. `2y – 3y^2`: Binomial
  6. `2y – 3y^2 + 4y^3`: Trinomial
  7. `5x – 4y + 3xy`: Trinomial
  8. `4z – 15z^2`: Binomial
  9. `ab + bc + cd + da`: Polynomial
  10. `pqr`: Mononomial
  11. `p^2q + pq^2`: Binomial
  12. `2p + 2q`: Binomial

Question 3: Add the following.

(i) `ab – bc, bc – ca, ca – ab`

Answer: `(ab - bc) + (bc - ca) + (ca-ab)`
`=ab + bc + ca - bc - ca - ab= 0`

(ii) `a – b + ab, b – c + bc, c – a + ac`

Answer: `=(a - b + ab) + (b - c + bc) + (c - a + ac)`
`= a + b + c + ab + bc + ca - b - c - a`
`= ab + bc + ca`

(iii) `2p^2q^2 – 3pq + 4, 5 + 7pq – 3p^2q^2`

Answer: `= (2p^2q^2 - 3pq + 4) + (5 + 7pq - 3p^2q^2)`
`= 2p^2q^2 - 3p^2q^2 - 3pq + 7pq + 4 + 5`
`= - p^2q^2 + 4pq + 9`

(iv) `l^2 + m^2`, `m^2 + n^2`, `n^2 + l^2`, `2lm + 2mn + 2nl`

Answer: `=(l^2 + m^2) + (m^2 + n^2)`` + (n^2 + l^2) + (2lm + 2mn + 2nl)`
`= l^2 + l^2 + m^2 + m^2 + n^2 + n^2 + 2lm + 2mn + 2nl`
`= 2l^2 + 2m^2 + 2n^2 + 2lm + 2mn + 2nl`

Question 4: (a) Subtract `4a – 7ab + 3b + 12` from `12a – 9ab + 5b – 3`

Answer: `(12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12)`
`= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12`
(signs are reversed after –sign once bracket is opened)
`= 8a - 2ab + 2b - 15`

Question 4: (b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

Answer: `(5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx)`
`= 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx`
`= 2xy - 7yz + 5zx + 10xyz`

Question 4: (c) Subtract `4p^2q – 3pq + 5pq^2 – 8p + 7q – 10` from `18 – 3p – 11q + 5pq – 2pq^2 + 5p^2q`

Answer: `(18 - 3p - 11q + 5pq - 2pq^2 + 5p^2q)`` - (4p^2q - 3pq + 5pq^2 - 8p + 7q - 10)`
`= 18 - 3p - 11q + 5pq - 2pq^2 ``+ 5p^2q - 4p^2q + 3pq - 5pq^2 + 8p - 7q + 10`
`= 28 + 5p - 18q + 8pq - 7pq^2 - p^2q`