NCERT SOLUTIONS FOR MATHS CLASS 8 ALGEBRAIC EXPRESSIONS AND IDENTITIES CHAPTER 9 Ex. 9.1

Question 1.
Identify the terms, their coefficients for each of the following expressions.
(i) 5xyz² – 3zy
(ii) 1 + x + x²
(iii) 4x²y² – 4x²y²z² + z²
(iv) 3 – pq + qr – rp
(v) x2 + y2 – xy
(vi) 0.3a – 0.6ab + 0.5b
Solution:

Question 2.
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
x + y, 1000, x + x² + x³ + x⁴, 7 + y + 5x, 2y – 3y², 2y – 3y² + 4y³, 5x – 4y + 3xy, 4z – 15z², ab + bc + cd + da, pqr, p²q + pq², 2p + 2q
Solution:

(iii) Given:
2p²q² – 3pq + 4, 5 + 7pq – 3p²q²
By arranging the like terms in the same column, we have

(Adding columnwise)

(iv) Given: l² + m², m² + n², n² + l², 2lm + 2mn + nl
By arranging the like terms in the same column, we have

Thus, the sum of the given expressions is 2(l² + m² + n² + lm + mn + nl)

Question 4.
(a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3
(6) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz
(c) Subtract 4p²q – 3pq + 5pq² – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq² + 5p²q
Solution:
(a) Arranging the like terms column-wise, we have

[Change the signs of all the terms of lower expressions and then add]
(b) Arranging the like terms column-wise, we have

[Change the signs of all the terms of lower expressions and then add]
(c) Arranging the like terms column-wise, we have

[Change the signs of all the terms of lower expressions and then add]
The terms are p²q – 7pq² + 8pq – 18q + 5p + 20