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) 5xyz² – 3zy
 (ii) 1 + x + x²
(iii) 4x²y² – 4x²y²z² + z²
 (iv) 3 – pq + qr – rp
 (v) (x/2) –(y/2) -xy
 (vi) 0.3a – 0.6ab + 0.5b
Answer:

No	Expression	Coefficient
1	Term: xyz2 Term: zy	5 -3
2	Term: 1 Term: x Term x2	1 1 1
3	Term: x2y2 Term: x2y2z2 Term z2	4 -4 1
4	3 pq qr rp	3 -1 1 -1
5	x Y xy	½ -1/2 -1
6	a ab b	.3 -.6 .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:
x + y: Binomial
1000: Monomial
x + x² + x³ + x⁴: Polynomial
7 + y + 5x: Binomial
2y – 3y²: Binomial
2y – 3y² + 4y³: Trinomial
5x – 4y + 3xy: Trinomial
4z – 15z²: Binomial
ab + bc + cd + da: Polynomial
pqr: Monomial
p²q + pq²: Binomial
2p + 2q: Binomial


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
Answer: i) (ab - bc) + (bc - ca) + (ca-ab)
= ab + bc + ca - bc - ca - ab
= 0
ii) (a - b + ab) + (b - c + bc) + (c - a + ac)
= a + b + c + ab + bc + ca - b - c - a
= ab + bc + ca
iii) 2p²q² – 3pq + 4, 5 + 7pq – 3p²q²
= (2p²q² - 3pq + 4) + (5 + 7pq - 3p²q²)
= 2p²q² - 3p²q² - 3pq + 7pq + 4 + 5
= - p²q² + 4pq + 9
iv) (l² + m²) + (m² + n²) + (n² + l²) + (2lm + 2mn + 2nl)
= l² + l² + m² + m² + n² + n² + 2lm + 2mn + 2nl
= 2l² + 2m² + 2n² + 2lm + 2mn + 2nl
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
Answer: While subtracting, we need to remember signs are reversed after –sign once bracket is opened
ie. + becomes - and - becomes +
Let solve the below question keeping that in mind
i) (12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12)
= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12
= 8a - 2ab + 2b - 15
ii) (5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx)
= 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx
= 2xy - 7yz + 5zx + 10xyz
iii) (18 - 3p - 11q + 5pq - 2pq² + 5p²q) - (4p²q - 3pq + 5pq² - 8p + 7q - 10)
= 18 - 3p - 11q + 5pq - 2pq² + 5p²q - 4p²q + 3pq - 5pq² + 8p - 7q + 10
= 28 + 5p - 18q + 8pq - 7pq² - p²q

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