NCERT solution class 8 chapter 9 Algebraic Expression and Identities exercise 9.1

Exercise 9.1

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Introduction - Algebraic Expressions and Identities - Chapter 9 - NCERT Class 8th Maths

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Q 1 - Ex 9.1 - Algebraic Expressions and Identities - NCERT Maths Class 8th - Chapter 9

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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)
(vi) 0.3a − 0.6ab + 0.5b

Sol :
The terms and the respective coefficients of the given expressions are as follows.

-	Terms	Coefficients
(i)	5xyz2 − 3zy	5 − 3
(ii)	1 x x2	1 1 1
(iii)	4x2y2 − 4x2y2z2 z2	4 − 4 1
(iv)	3 − pq qr − rp	3 −1 1 −1
(v)	− xy	− 1
(vi)	0.3a − 0.6ab 0.5b	0.3 − 0.6 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

Sol :
The given expressions are classified as
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 these categories are
x + x² + x³ + x⁴, ab + bc + cd + da

Q - 3 - Ex 9.1 - Algebraic Expressions and Identities - NCERT Maths Class 8th - Chapter 9

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Question 3
Add the following.
(i) ab − bc, bc − ca, ca − ab
(ii) a − b + ab, b − c + bc, c − a + ac
(iii) 2p²q² − 3pq + 4, 5 + 7pq − 3p²q²
(iv) l² + m², m² + n², n² + l², 2lm + 2mn + 2nl

Sol :
The given expressions written in separate rows, with like terms one below the other and then the addition of these expressions are as follows.
(i)

Thus, the sum of the given expressions is 0.
(ii)

Thus, the sum of the given expressions is ab + bc + ac.
(iii)

Thus, the sum of the given expressions is −p²q² + 4pq + 9.
(iv)

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

Q 4 - Ex 9.1 - Algebraic Expressions and Identities - NCERT Maths Class 8th - Chapter 9

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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 4p²q − 3pq + 5pq² − 8p + 7q − 10 from 18 − 3p − 11q + 5pq − 2pq² + 5p²q

Sol :
The given expressions in separate rows, with like terms one below the other and then the subtraction of these expressions is as follows.
(a)

(b)

(c)