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
^{2}q
^{2} - 4p
^{2}q
^{2}r
^{2}+ r
^{2}
(iv)4 - xy + yz - xz
(v) (x/4) - (y/5) -y
(vi)1.3a - 2.6ab + 1.5b
Solution
(i) Terms xyz^{2}, 3xy coefficients 1,3
(ii)Terms 1,-x,-2x^{2} Coefficients 1, -1,-2
(iii)Terms 4p^{2}q^{2},-4p^{2}q^{2}r^{2},r^{2} 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
^{2}q + pq
^{2}
(l) 2p + 2q+1
Solution
(a)x^{2} + y^{2}: Binomial
(b)1000-x:Binomial
(c)x + x^{2}+ x^{3} + x^{4} + x^{5}:polynomial
(d)8 - y -5x:Trinomial
(e) 2y -3y^{2}:Binomial
(f) 2y - 3y+ 4y^{3}:Trinomial
(g) 5x -8y + 3xy:Trinomial
(h) 4 -15z^{2}:Binomial
(i) ab + bc + cd + da+ 2ab:polynomial
(j) pqr+2pq+5pqr:Binomial
(k) p^{2}q + pq^{2}: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
^{2}q
^{2}- 3pq + 4, 5 + 7pq - 3p
^{2}q
^{2} ,4p
^{2}q
^{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)2p^{2}q^{2}- 3pq + 4 + 5 + 7pq - 3p^{2}q^{2} + 4p^{2}q^{2} + 10pq=3p^{2}q^{2}+14pq+9
(iv) a^{2}+ b^{2}+ b^{2}+ c^{2}+ c^{2}+ a^{2}+ 2ab + 2bc + 2ac=2(a^{2}+ b^{2}+c^{2}+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
^{2}q - 4pq - 5pq
^{2} - 8p + 7q - 18
from 18 - 3p - 11q + 5pq - 2pq
^{2}+ 5p
^{2}q
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 - 2pq^{2}+ 5p^{2}q -(4p^{2}q - 4pq - 5pq^{2} - 8p + 7q - 18)= 18 - 3p - 11q + 5pq - 2pq^{2}+ 5p^{2}q -4p^{2}q+4pq +5pq^{2}+8p-7q+18=36-3p-18q+9pq+3pq^{2}+5p^{2}q -4p^{2}q
Question 5
What are the coefficient of each term in the below expression?
4p
^{2}q
^{2} + 4p
^{2}q
^{2}r
^{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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