Class 8 - Mathematics
Algebraic Expressions and Identities - Exercise 9.2
Top Block 1
Question :1. Find the product of the following pairs of monomials:
(i) 4, 7p
(ii) -4p, 7p
(iii) -4p, 7pq
(iv) 4p³, -3p
(v) 4p, 0
(i) 4, 7p
(ii) -4p, 7p
(iii) -4p, 7pq
(iv) 4p³, -3p
(v) 4p, 0
Answer :
(i) 4 x 7p = 4 x 7 x p = 28p
(ii) -4p x 7p = (-4 x 7) x (p x p)
⇒ = -28p²
(iii) -4p x 7pq = (-4 x 7) x (p x pq)
⇒ = -28p²q
(iv) 4p³ X -3p = (4 X -3) (p³ X p)
⇒ = 12p4
(v) 4p X 0 = (4 X 0)(p)
⇒ = 0
(i) 4 x 7p = 4 x 7 x p = 28p
(ii) -4p x 7p = (-4 x 7) x (p x p)
⇒ = -28p²
(iii) -4p x 7pq = (-4 x 7) x (p x pq)
⇒ = -28p²q
(iv) 4p³ X -3p = (4 X -3) (p³ X p)
⇒ = 12p4
(v) 4p X 0 = (4 X 0)(p)
⇒ = 0
Question :2. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively: (p, q); (10m, 5n); (20x², 5y²); (4x, 3x²) (3mn, 4np)
Answer :
(i) Area of rectangle
⇒ = length x breadth
⇒ = p x q = pq sq. units
(ii) Area of rectangle
⇒ = length x breadth
⇒ = 10m x 5n = 50mn sq. units
(iii) Area of rectangle = length x breadth
⇒ = 20x² X 5y²
⇒ = (20 x 5) (x² X y²)
⇒ = 100x²y² sq. units
(iv) Area of rectangle = length x breadth
⇒ = 4x X 3x² = (4 x 3)(x X x²)
⇒ = 12x³ sq. units
(v) Area of rectangle = length x breadth
⇒ = 3mn x 4np = (3 x 4)(mn x np)
⇒ = 12mn²p sq. units
(i) Area of rectangle
⇒ = length x breadth
⇒ = p x q = pq sq. units
(ii) Area of rectangle
⇒ = length x breadth
⇒ = 10m x 5n = 50mn sq. units
(iii) Area of rectangle = length x breadth
⇒ = 20x² X 5y²
⇒ = (20 x 5) (x² X y²)
⇒ = 100x²y² sq. units
(iv) Area of rectangle = length x breadth
⇒ = 4x X 3x² = (4 x 3)(x X x²)
⇒ = 12x³ sq. units
(v) Area of rectangle = length x breadth
⇒ = 3mn x 4np = (3 x 4)(mn x np)
⇒ = 12mn²p sq. units
Question :3. Complete the table of products:
(i)
(i)
Answer :
(i)
(i)
Mddle block 1
Question :4. Obtain the volume of rectangular boxes with the following length, breadth and height respectively:
(i) 5a, 3a², 7a4
(ii) 2p, 4q, 8r
(iii) xy, 2x²y, 2xy²
(iv) a, 2b, 3c
(i) 5a, 3a², 7a4
(ii) 2p, 4q, 8r
(iii) xy, 2x²y, 2xy²
(iv) a, 2b, 3c
Answer :
(i) Volume of rectangular box= length X breadth X height
⇒ = 5a X 3a² X 7a4
⇒ = (5 x 3 x 7)(a x a² x4)
⇒ = 105a7cubic units
(ii) Volume of rectangular box
⇒ = length X breadth X height
⇒ = 2p x 4q x 8r
⇒ = 64pqr cubic units
(iii) Volume of rectangular box
⇒ = length X breadth X height
⇒ = xy X 2x²y X 2xy²
⇒ = (1 x 2 x 2)(x X x² X x X y X y X y²)
⇒ = 4x4y4cubic units
(iv) Volume of rectangular box
⇒ = length X breadth X height
⇒ = a x 2b x 3c
⇒ = (1 x 2 x 3) (a x b x c)
⇒ = 6abc cubic units
(i) Volume of rectangular box= length X breadth X height
⇒ = 5a X 3a² X 7a4
⇒ = (5 x 3 x 7)(a x a² x4)
⇒ = 105a7cubic units
(ii) Volume of rectangular box
⇒ = length X breadth X height
⇒ = 2p x 4q x 8r
⇒ = 64pqr cubic units
(iii) Volume of rectangular box
⇒ = length X breadth X height
⇒ = xy X 2x²y X 2xy²
⇒ = (1 x 2 x 2)(x X x² X x X y X y X y²)
⇒ = 4x4y4cubic units
(iv) Volume of rectangular box
⇒ = length X breadth X height
⇒ = a x 2b x 3c
⇒ = (1 x 2 x 3) (a x b x c)
⇒ = 6abc cubic units
5. Obtain the product of:
(i) xy, yz, zx
(ii) a, -a², a³
(iii) 2, 4y, 8y², 16y³
(iv) a, 2b, 3c, 6abc
(v) m, -mn, mnp
(i) xy, yz, zx
(ii) a, -a², a³
(iii) 2, 4y, 8y², 16y³
(iv) a, 2b, 3c, 6abc
(v) m, -mn, mnp
Answer :
(i) xy X yz X zx = x X x X y X y X z X z
⇒ = x²y²z²
(ii) a x (-a)² x a³ = (-1)(a x a² x a³)
⇒ = -a6
(iii) 2 x 4y x 8y² x 16y³
⇒ = (2 x 4 x 8 x 16)(y x y² x y³)
⇒ = 1024y6
(iv) a x 2b x 3c x 6abc
⇒ = (1 x 2 x 3 x 6)(a x b x c x abc)
⇒ = 36a²b²c²
(v) m x –mn x mnp
⇒ =(-1)(m x m x m x n x n x p)
⇒ = -m³n²p
(i) xy X yz X zx = x X x X y X y X z X z
⇒ = x²y²z²
(ii) a x (-a)² x a³ = (-1)(a x a² x a³)
⇒ = -a6
(iii) 2 x 4y x 8y² x 16y³
⇒ = (2 x 4 x 8 x 16)(y x y² x y³)
⇒ = 1024y6
(iv) a x 2b x 3c x 6abc
⇒ = (1 x 2 x 3 x 6)(a x b x c x abc)
⇒ = 36a²b²c²
(v) m x –mn x mnp
⇒ =(-1)(m x m x m x n x n x p)
⇒ = -m³n²p