These NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1

Question 1.

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

(i) 5xyz^{2} – 3zy

(ii) 1 + x + x^{2}

(iii) 4x^{2}y^{2} – 4x^{2}y^{2}z^{2} + z^{2}

(iv) 3 – pq + qr – rp

(v) \(\frac{x}{2}+\frac{y}{2}\) – xy

(vi) 0.3a – 0.6ab + 0.5b

Solution:

(i) 5xyz^{2} – 3zy

Terms are 5xyz^{2} and -3zy

Coefficients of 5xyz^{2} is 5

Coefficients of-3zy is -3

(ii) 1 + x + x^{2}

Terms are x^{2}, x, and 1

Coefficient of x^{2} is 1

coefficient of x is 1

and constant term is 1

(iii) 4x^{2}y^{2} – 4x^{2}y^{2}z^{2} + z^{2}

Terms are 4x^{2}y^{2}, -4x^{2}y^{2}z^{2} and z^{2}

Coefficient of x^{2}y^{2} is 4

Coefficient of -4x^{2}y^{2}z^{2} is -4

Coefficient of z^{2} is 1

(iv) 3 – pq + qr – rp

Terms are 3, -pq, qr and -rp

Coefficient of 3 is 3.

Coefficient of -pq is -1.

Coefficient of qr is 1 and coefficient of -rp is -1

(v) \(\frac{x}{2}+\frac{y}{2}\) – xy

Terms are \(\frac{x}{2}, \frac{y}{2}\) and -xy

Coefficient of \(\frac{\mathrm{x}}{2}\) is \(\frac{1}{2}\)

Coefficient of \(\frac{\mathrm{x}}{2}\) is \(\frac{1}{2}\)

and coefficient of -xy is -1

(vi) 0.3a – 0.6ab + 0.5b

Terms are 0.3a, -0.6ab and 0.5b

Coefficient of 0.3a is 0.3

Coefficient of -0.6ab is -0.6

Coefficient of 0.5b is 0.5

Question 2.

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

x + y, 1000, x + x^{2} + x^{3} + x^{4}, 7 + y + 5x, 2y – 3y^{2}, 2y – 3y^{2} + 4y^{3}, 5x – 4y + 3xy, 4z – 15z^{2}, ab + bc + cd + da, pqr, p^{2}q + pq^{2}, 2p + 2q

Solution:

Monomials: 100pqr

Binomials: x + y; 2y – 3y^{2}; 4z – 15z^{2}; p^{2}q + pq^{2}; 2p + 2q

Trinomials: 7 + y + 5x; 2y – 3y^{2} + 4y^{3}; 5x – 4y + 3xy

Polynomials that do not fit in these categories: x + x^{2} + x^{3} + x^{4} and ab + bc + cd + da

(Since the above polynomials has four terms)

Question 3.

Add the following.

(i) ab – bc, bc – ca, ca – ab

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

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

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

Solution:

(i) ab – bc; bc – ca; ca – ab

(ii) a – b + ab; b – c + bc; c – a + ac

(iii) 2p^{2}q^{2} – 3pq + 4; 5 + 7pq – 3p^{2}q^{2}

(iv) l^{2} + m^{2}; m^{2} + n^{2}; n^{2} + l^{2}; 2lm + 2mn + 2nl

= 2(l^{2} + m^{2} + n^{2} + lm + mn + nl)

Question 4.

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

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

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

Solution: