In this page we have Important questions for Algebraic Expressions and Identities Class 8 Maths Chapter 9 . Hope you like them and do not forget to like , social share
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Question 1
Identify the terms, their coefficients for each of the following expressions.
(i)xyz
2 + 3xy
(ii)1 - x -2x
2
(iii)4p
2q
2 - 4p
2q
2r
2+ r
2
(iv)4 - xy + yz - xz
(v) (x/4) - (y/5) -y
(vi)1.3a - 2.6ab + 1.5b
Solution
(i) Terms xyz2, 3xy coefficients 1,3
(ii)Terms 1,-x,-2x2 Coefficients 1, -1,-2
(iii)Terms 4p2q2,-4p2q2r2,r2 Coefficients 4,-4,1
(iv) Terms 4,-xy,yz,-xz Coefficients 4,-1,1,-1
(v) Terms x/4, -y/5 ,-y Coefficients 1/4,-1/5,-1
(vi) Terms 1.3a,-2.6ab,1.5b Coefficients 1.3,-2.6 ,1.5
Question 2
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
(a)x
2 + y
2
(b)1000-x
(c)x + x
2+ x
3 + x
4 + x
5
(d)8 - y -5x
(e) 2y -3y
2
(f) 2y - 3y+ 4y
3
(g) 5x -8y + 3xy
(h) 4 -15z
2
(i) ab + bc + cd + da+ 2ab
(j) pqr+2pq+5pqr
(k) p
2q + pq
2
(l) 2p + 2q+1
Solution
(a)x2 + y2: Binomial
(b)1000-x:Binomial
(c)x + x2+ x3 + x4 + x5:polynomial
(d)8 - y -5x:Trinomial
(e) 2y -3y2:Binomial
(f) 2y - 3y+ 4y3:Trinomial
(g) 5x -8y + 3xy:Trinomial
(h) 4 -15z2:Binomial
(i) ab + bc + cd + da+ 2ab:polynomial
(j) pqr+2pq+5pqr:Binomial
(k) p2q + pq2:Binomial
(l) 2p + 2q+1:Trinomial
Question 3
Add the following.
(i) ab - bc+ ac, bc - ca+ ab, ca - ab-2bc
(ii)p - q + pq, q - r + qr, r - p + pr , p+q+r
(iii)2p
2q
2- 3pq + 4, 5 + 7pq - 3p
2q
2 ,4p
2q
2 + 10pq
(iv)a
2+ b
2, b
2+ c
2, c
2+ a
2, 2ab + 2bc + 2ac
Solution
(i) ab - bc+ ac + bc - ca+ ab +ca - ab-2bc=ab-2bc+ac
(ii)p - q + pq + q - r + qr + r - p + pr + p+q+r=p+q+pq+r+qr+pr
(iii)2p2q2- 3pq + 4 + 5 + 7pq - 3p2q2 + 4p2q2 + 10pq=3p2q2+14pq+9
(iv) a2+ b2+ b2+ c2+ c2+ a2+ 2ab + 2bc + 2ac=2(a2+ b2+c2+ab+bc+ac)
Question 4.
(a) Subtract 8a - 7ab + 3b - 20 from 20a - 9ab + 5b - 20
(b) Subtract 3pq + 5qr - 7pr+1 from -4pq +2qr - 2pr + 5pqr+1
(c) Subtract 4p
2q - 4pq - 5pq
2 - 8p + 7q - 18
from 18 - 3p - 11q + 5pq - 2pq
2+ 5p
2q
Solution
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
(a) 20a - 9ab + 5b - 20 -(8a - 7ab + 3b - 20)=20a - 9ab + 5b - 20-8a +7ab-3b+20 =12a+2b -2ab
(b) -4pq +2qr - 2pr + 5pqr+1 -( 3pq + 5qr - 7pr+1 )=-4pq +2qr - 2pr + 5pqr+1 -3pq-5qr+7pr-1=-7pq -3qr+5pr+5pqr
(c) 18 - 3p - 11q + 5pq - 2pq2+ 5p2q -(4p2q - 4pq - 5pq2 - 8p + 7q - 18)= 18 - 3p - 11q + 5pq - 2pq2+ 5p2q -4p2q+4pq +5pq2+8p-7q+18=36-3p-18q+9pq+3pq2+5p2q -4p2q
Question 5
What are the coefficient of each term in the below expression?
4p
2q
2 + 4p
2q
2r
2 - r
2 +5
(a)4,4,-1,5
(b)4,4,1,5
(c) 4,4r
2 ,-r
2, 5
(d) None of these
Solution
Answer is (a)
Question 6
The product of a monomial and trinomial will be a
(a)monomial
(b)trinomial
(c)binomial
(d) None of these
Solution
Answer is (b)
Question 7
The exponents of a variable term in the polynomial is a
(a) integers
(b)negative integers
(c) positive integers
(d) non -negative integers
Solution
Answer is (d)
Question 8
The expression pqr +rqp+qpr is a
(a) Monomial
(b)trinomial
(c) binomial
(d) none of these
Solution
Answer is (a) as it sums to 3pqr
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