RBSE Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.1

Rajasthan Board RBSE Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.1 Textbook Exercise Questions and Answers.

RBSE Class 8 Maths Solutions Chapter 9 Algebraic Expressions and Identities Ex 9.1

Question 1.
Identify the terms, their coefficients for each of the following expressions. 
(i) 5xyz² - 3zy
Answer:
In the expression 5xyz2² - 3zy, the terms are 5xyz² and - 3zy.
Coefficient of xyz² in the term 5xyz² is 5.
Coefficient of zy in the term - 3zy is - 3.

(ii) 1 + x + x²
Answer:
In the expression 1 + x + x², the terms are 1, x and x².
Coefficient of term 1 is 1.
Coefficient of term x is 1.
Coefficient of term x² is 1.

(iii) 4x²y² - 4x²y²z² + z²
Answer:
In the expression 4x²y² - 4x²y²z² + z², the terms are 4x²y², - 4x²y²z² and z²
Coefficient of x²y² in the term 4x²y² is 4.
Coefficient of x²y²z² in the term x²y²z² is - 4.
Coefficient of z² in the term z² is 1.

(iv) 3 - pq + qr - rp
Answer:
In the expression 3 - pq + qr - rp, the terms are 3, - pq, qr and - rp.
Coefficient of term 3 is 3.
Coefficient of pq in the term - pq is - 1.
Coefficient of qr in the term qr is 1.
Coefficient of rp in the term - rp is - 1.

(v) \(\frac{x}{2}+\frac{y}{2}\) - xy
Answer:
In the expression \(\frac{x}{2}+\frac{y}{2}\) - xy, the terms are \(\frac{x}{2}, \frac{y}{2}\) and - xy.
Coefficient of x in the term \(\frac{x}{2}\) is \(\frac{1}{2}\).
Coefficient of y m the term \(\frac{y}{2}\) is \(\frac{1}{2}\)
Coefficient of xy in the term - xy is - 1.

(vi) 0.3a - 0.6ab + 0.5b
Answer:
In the expression 0.3a - 0.6ab + 0.5b, the terms are 0.3a, - 0.6ab and 0.5b.
Coefficient of a in the term 0.3a is 0.3.
Coefficient of ab in the term - 0.6ab is - 0.6.
Coefficient of b in the term 0.56 is 0.5.

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
Answer:
The given polynomials are classified as below:
Monomials : 1000, pqr
Binomials : x + y, 2y - 3y², 4z - 15z², p²q + pq², 2p + 2q
Trinomials : 7 + y + 5x, 2y - 3y² + 4y³, 5x - 4y + 3xy
Polynomials that do not fit in any of there three categories:
x + x² + x³ + x⁴ , ab + bc + cd + da.

Question 3.
Add the following.
(i) ab - bc, bc - ca, ca - ab
(ii) a - b + ab, b - c + be, c - a + ac
(iii) 2p²q² - 3pq + 4, 5 + 7pq - 3p²q²
(iv) l² + m², m² + n², n² + l², 2lm + 2mn + 2nl
Answer:
(i) Writing the given expressions in separate rows with like terms one below the other, we have

(ii) Writing the given expressions in separate rows with like terms one below the other, we have

(iii) Writing the given expressions in separate rows with like terms one below the other, we have

(iv) Writing the given expressions in separate rows with like terms one below the other, we have

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^2q - 3pq + 5pq² - 8p + 7q - 10 from 18 - 3p - 11q + 5pq - 2pq² + 5p²q.
Answer:
Rearranging the terms of the given expressions, changing the sign of each term of the expression to be subtracted and adding the two expressions, we get