Q.1. Get the algebraic expressions in the following cases using variables, constants, and arithmetic operations:
(i) Subtraction of z from y.
Ans: y  z
(ii) Onehalf of the sum of numbers x and y.
Ans: (x + y)/2
(iii) The number z multiplied by itself.
Ans: Z^{2}
(iv) Onefourth of the product of numbers p and q.
Ans: pq/4
(v) Numbers x and y both squared and added.
Ans: x^{2} + y^{2}
(vi) Number 5 added to three times the product of m and n.
Ans: 3mn + 5
(vii) A product of numbers y and z subtracted from 10.
Ans: 10  yz
(viii) Sum of numbers a and b subtracted from their product.
Ans: ab  (a + b)
Q.2. (i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:
(a) x  3
Ans:
(b) 1 + x + x^{2}
^{Ans: }
(c) y  y^{3}
^{Ans: }
(d) 5xy^{2} + 7x^{2}y
Ans:
(e) ab + 2b^{2}  3a^{2}
^{Ans: }
(a) 4x + 5
(b) 4x + 5y
Ans:
Terms: 4x, 5y
Factors: 4,x ; 5,y
(c) 5y + 3y^{2}
Ans:
Terms: 5y,3y^{2}
Factors: 5, y ; 3,y,y
(d) xy + 2x^{2}y^{2}
Ans:
Terms: xy, 2x^{2}y^{2}
Factors: x, y ; 2x, x, y, y
(e) pq + q
Ans:
Terms: pq, q
Factors: p, q ; q
(f) 1.2ab  2.4b + 3.6a
Ans:
Terms: 1,2ab.2.4b,3 6a
Factors: 1.2.a.b ; 2.4,6 ; 3.6,a
(g)
Ans:
(h) 0.1 p^{2} + 0.2q^{2}
Ans:
Terms: 0.1 p^{2},0.2q^{2}
Factors: 0. 1,p,p, ; 0.2, q,q
Q.3. Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5  3t^{2}
(ii) 1 + t + t^{2} + t^{2}
(iii) x + 2xy + 3y
(iv) 100m + 1000n
(v) p^{2}q^{2} + 7pq
(vi) 1.2a + 0.8b
(vii) 3.14 r^{2}
(viii) 2(l + b)
(ix) 0.1y + 0.01y^{2}
^{Ans: }
Q.4. (a) Identify terms which contain x and give the coefficient of x.
(i) y^{2}x + y
(ii) 13y^{2}  8yx
(iii) x + y + 2
(iv) 5 + z + zx
(v) 1 + x + xy
(vi) 12xy^{2} + x25
(vii) 7x + xy^{2}
Ans:
(b) Identify terms which contain y^{2} and give the coefficient of y^{2.}
(i) 8  xy^{2}
(ii) 5y^{2} + 7x
(iii) 2x^{2}y  15xy^{2} + 7y^{2}
Ans:
Q.5. Classify into monomials, binomials and trinomials:
(i) 4y  7x
(ii) y^{2}
(iii) x + y  xy
(iv) 100
(v) ab  a  b
(vi) 5  3t
(vii) 4p^{2}q  4pq^{2}
(viii) 7mn
(ix) z^{2}  3z + 8
(x) a^{2} + b^{2}
(xi) z^{2} + z
(xii) 1 + x + x^{2}
^{Ans: }
Q.6. State whether a given pair of terms is of like or unlike terms:
(i) 1,100
(ii)
(iii) 29x, 29y
(iv) 14xy, 42 yx
(v) 4m^{2}p, 4mp^{2}
(vi) 12xz, 12x^{2} z^{2}
^{Ans: }
Q.7. Identify like terms in the following:
(a) xy^{2}, 4yx^{2}, 8x^{2}, 2xy^{2}, 7y, 11x^{2}  100x,  11yx, 20x^{2}y, 6x^{2}, y, 2xy, 3x
Ans: Like terms are:
(i) xy^{2},2 xy^{2}
(ii) 4yx^{2} , 20x^{2}y
(iii) 8x^{2},11x^{2},6x^{2}
(iv) 7y, y
(v) 100x, 3x
(vi) 11yx, 2xy
(b) 10pq, 7p, 8q, p^{2}q^{2}, 7qp, 100q, 23, 12q^{2}p^{2}, 5p^{2}, 41,2405 p, 78qp, 13p^{2}q, qp^{2}, 701p^{2}
^{Ans: Like terms are:}
(i) 10 pq  7 pq,78 pq
(ii) 7p, 2405 p
(iii) 8q, 100q
(iv) p^{2}q^{2}, 12p^{2}q^{2}
(v) 12,41
(vi) 5p^{2},701p^{2}
(vii) 13 p^{2}q,qp^{2}
Q1: If m = 2, find the value of:
(i) m  2
(ii) 3m  5
(iii) 9  5m
(iv) 3m^{2}  2m  7
(v)
Ans:
(i) m  2 = 2  2 [Putting m = 2]
= 0
(ii) 3m  5 = 3 x 2  5 [Putting m = 2]
= 6  5 = 1
(iii) 9  5m = 9  5 x 2 [Putting m = 2]
= 9  10 =  1
(iv) 3m^{2}  2m  7
= 3(2)^{2}  2 (2)  7 [Putting m = 2]
= 3 x 4  2 x 2  7
= 1247
= 12 11 = 1
(v) [Putting m = 2]
= 5  4 = 1
Q2: If p = 2, find the value of:
(i) 4p + 7
(ii)  3p^{2} + 4p + 7
(iii) 2p^{3}  3p^{2} +4/7 + 7
Ans:
(i) 4p + 7 = 4 ( 2) + 7 [Putting p= 2]
= 8 + 7 = 1
(ii) 3p^{2}+4p + 7
= 3 (2)^{2}+ 4 (2) + 7 [Putting p =  2]
=  3 x 4  8 + 7
=  12  8 + 7
= 20 + 7 = 13
(iii)  2p^{3}  3p^{2} +4p + 7
=  2 (2)^{3}  3(2)^{2 }+ 4 (2) + 7 [Putting p =  2]
= 2 x(8)3 x4 8 + 7
= 16128 + 7
= 20 + 23 = 3
Q3: Find the value of the following expressions, when x = 1:
(i) 2x  7
(ii) x + 2
(iii) x^{2} + 2x + 1
(iv) 2x^{2} x  2
Ans:
(i) 2x  7 = 2 (1)  7 [Putting x=  1]
=  2  7 =  9
(ii)  x + 2 =  (1) + 2 [Putting x=  1]
= 1 + 2 = 3
(iii) x^{2} + 2 x + 1 = (1)^{2} + 2 (1) + 1 [Putting x=  1]
= 1  2 + 1
= 2  2 = 0
(iv) 2x^{2} x  2 = 2 (1)^{2}  (1)  2 [Putting x=  1]
= 2x1 + 12
= 2 + 1  2
= 3  2 = 1
Q4: If a = 2,b = 2, find the value of:
(i) a^{2} + b^{2 }
(ii) a^{2}+ab + b^{2}
(iii) a^{2}  b^{2}
Ans:
(i) a^{2} + b^{2} ( 2)^{2} + ( 2)^{2} [Putting a = 2. b =  2 ]
= 4 + 4 = 8
(ii) a^{2}+ab + b^{2 }
= (2) + ( 2) ( 2) +(2)^{2 }[Putting a = 2. b =  2 ]
= 4  4 + 4 = 4
(iii) a^{2}  b^{2} = (2)^{2}  (2)^{2} [Putting a = 2,b =  2]
= 4  4 = 0
Q5: When a = 0, b = 1, find the value of the given expressions:
(i) 2a + 2b
(ii) 2a^{2}+b^{2}+1
(iii) 2a^{2}b + 2ab^{2} +ab
(iv) a^{2}+ab+2
Ans:
(i) 2a + 2b = 2 (0) + 2 (1) [Putting a  0,b =  1]
= 0  2 = 2
(ii) 2a^{2} + b^{2} + 1 = 2 (0)^{2} + (1)^{2} + 1 [Putting a  0,b =  1]
= 2 x 0 + 1+ 1 = 0 + 2 = 2
(iii) 2a^{2}b + 2ab^{2} + ab = 2(0)^{2} (1) + 2 (0 )(1)^{2} + (0 )(1) [Putting a  0,b =  1]
= 0 + 0 + 0 = 0
(iv) a^{2} +ab + 2  (0)^{2} + (0) (1) + 2 [Putting a  0,b =  1]
= 0 + 0 + 2 = 2
Q6: Simplify the expressions and find the value if x is equal to 2:
(i) x + 7 + 4 (x 5)
(ii) 3 (x + 2) + 5x  7
(iii) 6x + 5 (x  2)
(iv) 4 (2x  1) + 3x + 11
Ans:
(i) x + 7 + 4(x 5) = x + 7 + 4x  20 = x + 4 x + 7  20
= 5 x  13 = 5 x 2  13 [Putting x = 2]
= 1013 = 3
(ii) 3 (x+ 2) + 5x  7 = 3x + 6 + 5x 7 = 3x + 5x + 6  7
= 8x  1 = 8 x 21 [Putting x = 1]
= 16  1 = 15
(iii) 6x + 5 (x  2) = 6x + 5x 10 = 11x  10
= 11 x 2  10 [Putting x = 1]
= 22  10 = 12
(iv) 4(2x  1) + 3x + 11 = 8x  4 + 3x +11 = 8x + 3a  4 + 11
= 11a + 7 = 11 x 2 + 7 [Putting x =  1]
= 22+7 = 29
Q7: Simplify these expressions and find their values if x = 3,a = 1, b =  2 :
(i) 3x  5  x + 9
(ii) 2  8x + 4x + 4
(iii) 3a + 5  8a + 1
(iv) 10  3b  4  5b
(v) 2a  2b  4  5 + a
Ans:
(i) 3a  5  x + 9 = 3x  x  5 + 9 = 2x + 4
= 2x3+4 [Putting a = 3]
= 6 + 4 = 10
(ii) 2  8x + 4x + 4 =  8x + 4x + 2 + 4 = 4x + 6
=  4 x 3 + 6 [Putting a = 3]
= 12 + 6 =12
(iii) 3a + 5  8a + 1 = 3a  8a + 5 + 1 =  5a + 6
= 5( 1) + 6 [Putting a =  1]
= 5 + 6 = 11
(iv) 10  3b  4  5b =  3b  5b + 10  4 = 8b+6
= 8 (2)+ 6 [Putting b = 2]
= 16 + 6 = 22
(v) 2a  2b  4  5 + a = 2a + a  2b  4  5
= 3a  2b  9 = 3 (1)2 (2) 9 [Putting a = 1 , b =  2]
= 3 + 4 9 = 8
Q8:
(i) If z = 10, find the value of z^{3}  3 (z  10).
(ii) If p =  10, find the value of p^{2}  2p  100
Ans:
(i) z^{3} 3(z10) = (10)^{3}3(10  10) [Putting z = 10]
= 1000  3 x 0 = 1000 0
= 1000
(ii) p^{2}  2p  100 = (10)^{2}  2 (10)  100 (Putting p =  10]
= 100+ 20  100 = 20
Q9: What should be the value of a if the value of 2x^{2} + x  a equals to 5, when x = 0 ?
Ans:
Given: 2x^{2} + x  a = 5
⇒ 2 (0)^{2} + 0  a = 5 [Putting x = 0]
⇒ 0 + 0  a = 5
⇒ a = 5
Hence, the value of a is 5.
Q10: Simplify the expression and find its value when a = 5 and b =  3: 2 (a^{2} + ab) + 3  ab
Ans:
Given: 2 (a^{2} + ab) + 3  ab
⇒ 2a^{2} + 2ab + 3  ab
⇒ 2a^{2} + 2ab  ab + 3
⇒ 2a^{2} + ab + 3
⇒ 2 (5)^{2} + (5) (3) + 3 [Putting a = 5 , b = 3]
⇒ 2 x 25  15 + 3
⇒ 50  15 + 3
⇒ 38
76 videos345 docs39 tests

1. What are algebraic expressions? 
2. How do you simplify algebraic expressions? 
3. What is the difference between an algebraic expression and an algebraic equation? 
4. How can algebraic expressions be used in reallife situations? 
5. Can you give an example of a complex algebraic expression and how to simplify it? 

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