Class 6 - Mathematics
Chapter - Algebraic Expressions : Exercise 12.3
Top Block 1
Question : 1.If m=2, find the value of:
(i) m – 2
(ii) 3m – 5
(iii) 9 – 5m
(iv) 3m2 – 2m – 7
(v) 5m2 – 4
Answer :
(i) m – 2 = 2 – 2 [Putting m=2]
= 0
(ii) 3m – 5 = 3×2 – 5 [Putting m=2]
= 6 – 5 = 1
(iii) 9 – 5m = 9 – 5 x 2 [Putting m=2]
= 9 – 10 = – 1
(iv) 3m2 – 2m – 7 = 3(2)2 – 2(2) – 7 [Putting m=2]
= 3 x 4 – 2 x 2 – 7 = 12 – 4 – 7
= 12 – 11 = 1
(v) 5m⁄2 – 4 = 5 x 2⁄2 – 4 [Putting m=2]
= 5 – 4 = 1
Question : 2. If p = – 2, find the value of:
(i) 4p + 7
(ii) – 3p2 + 4p + 7
(iii) – 2p3 – 3p2 + 4p + 7
Answer :
(i) 4p + 7 = 4( –2) + 7 [Putting p= – 2]
= –8 + 7 = – 1
(ii) – 3p2 + 4p + 7 = –3( – 2)2 + 4( – 2) + 7 [Putting p= – 2]
= –3×4 – 8 + 7 = – 12 – 8 + 7
= –20 + 7 = – 13
(iii) – 2p3 – 3p2 + 4p + 7 = –2( – 2)3 – 3( – 2)2+ 4( – 2) + 7 [Putting p= – 2]
= = –2×( – 8) – 3×4 – 8 + 7 = 16 – 12 – 8 + 7
= – 20 + 23 = 3
Question : 3.Find the value of the following expressions, when 𝓍= – 1:
(i) 2𝓍 – 7
(ii) – 𝓍 + 2
(iii) 𝓍2 + 2𝓍 + 1
(iv) 2𝓍2 – 𝓍 – 2
Answer :
(i) 2𝓍 – 7 = 2( –1) – 7 [Putting 𝓍= – 1]
= –2 – 7 = – 9
(ii) – 𝓍 + 2 = –( – 1) + 2 [Putting 𝓍= – 1]
= 1 + 2 = 3
(iii) 𝓍2 + 2𝓍 + 1 = ( – 1)2 + 2( – 1) + 1 [Putting 𝓍= – 1]
= 1 – 2 + 1 = 2 – 2 = 0
(iv) 2𝓍2 – 𝓍 – 2 = 2( – 1)2 – ( – 1) – 2 [Putting 𝓍= – 1]
= 2 x 1 + 1 – 2 = 2 + 1 – 2
= 3 – 2
= 1
Question : 4.If a = 2, b = – 2, find the value of:
(i) a2 + b2
(ii) a2 + ab + b2
(iii) a2 – b2
Answer :
(i) a2 + b2 = (2)2 + ( – 2)2 [Putting a = 2, b = – 2]
= 4 + 4 = 8
(ii) a2 + ab + b2 = (2)2 + (2)( – 2) + ( – 2)2 [Putting a = 2, b = – 2]
= 4 – 4 + 4 = 4
(iii) a2 – b2 = (2)2 – ( – 2)2 [Putting a = 2, b = – 2]
= 4 – 4 = 0
Question : 5.When a=0,b= – 1, find the value of the given expressions:
(i) 2a + 2b
(ii) 2a2 + b2 + 1
(iii) 2a2b + 2ab2 + ab
(iv) a2 + ab + 2
Answer :
(i) 2a + 2b = 2(0) + 2( –1) [Putting a=0,b= – 1]
= 0 – 2 = – 2
(ii) 2a2 + b2 + 1 = 2(0)2 + ( –1)2 + 1 [Putting a=0,b= – 1]
= 2 x 0 + 1 + 1 = 0 + 2 = 2
(iii) 2a2b + 2ab2 + ab = 2(0)2( –1) + 2(0)( – 1)2 + (0)( – 1) [Putting a=0,b= – 1]
= 0 + 0 + 0 = 0
(iv) a2 + ab + 2 = (0)2 + (0)( – 1) + 2 [Putting a=0,b= – 1]
= 0 + 0 + 2 = 2
Question : 6.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
Answer :
(i) 𝓍 + 7 + 4(𝓍 – 5) = 𝓍 + 7 + 4𝓍 – 20 = 𝓍 + 4𝓍 + 7 – 20
= 5𝓍 – 13 = 5 x 2 – 13 [Putting 𝓍=2]
= 10 – 13 = –3
(ii) 3(𝓍 + 2) + 5𝓍 – 7 = 3𝓍 + 6 + 5𝓍 – 7 = 3𝓍 + 5𝓍 + 6 – 7
= 8𝓍 – 1 = 8 𝓍2 – 1 [Putting 𝓍= – 1]
= 16 – 1 = 15
(iii) 6𝓍 + 5(𝓍 – 2) = 6𝓍 + 5𝓍 – 10 = 11𝓍 – 10
= 11 𝓍2 – 10 [Putting 𝓍= – 1]
= 22 – 10 = 12
(iv) 4(2𝓍 – 1) + 3𝓍 + 11 = 8𝓍 – 4 + 3𝓍 + 11 = 8𝓍 + 3𝓍 – 4 + 11
= 11𝓍 + 7 = 11 𝓍2 + 7 [Putting 𝓍= – 1]
= 22 + 7 = 29
Mddle block 1
Question : 7.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
Answer :
(i) 3𝓍 – 5 – 𝓍 + 9 = 3𝓍 – 𝓍 – 5 + 9 = 2𝓍 + 4
= 2×3 + 4 [Putting 𝓍=3]
= 6 + 4 = 10
(ii) 2 – 8𝓍 + 4𝓍 + 4 = –8𝓍 + 4𝓍 + 2 + 4 = – 4𝓍 + 6
= –4×3 + 6 [Putting 𝓍=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
Question : 8.
(i) If z=10, find the value of z3 – 3(z – 10).
(ii) If p= – 10, find the value of p2 – 2p – 100.
Answer :
(i) z3 – 3(z – 10) = (10)3 – 3(10 – 10) [Putting z=10]
= 1000 – 3 𝓍 0 = 1000 – 0 = 1000
(ii) p2 – 2p – 100 = ( – 10)2 – 2( – 10) – 100 [Putting p= – 10]
= 100 + 20 – 100 = 20
Question : 9.What should be the value of 𝒶 if the value of 2𝓍2 + 𝓍 – 𝒶 equals to 5, when &x scr; =0 ?
Answer :
Given: 2𝓍2 + 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.
Question : 10.Simplify the expression and find its value when a=5 and b= – 3:2(a2 + ab) + 3 – ab
Answer :
Given: 2(a2 + ab) + 3 – ab
⇒ 2a2 + 2ab + 3 – ab ⇒ 2a2 + 2ab – ab + 3
⇒ 2a2 + ab + 3
⇒ 2(5)2 + (5)( – 3) + 3 [Putting a=5, b= – 3]
⇒ 2 𝓍25 – 15 + 3
⇒50 – 15 + 3
⇒ 38