Q. In the packet of 8 cm × 8 cm × 8 cm how many box match box will come of total volume of 2 cm × 2 cm × 2 cm?

Class 8th 
Maths

Q. In the packet of 8 cm × 8 cm × 8 cm how many box match box will come of total volume of 2 cm ×  2 cm × 2 cm?
Sol
                                  Vol. of Packet
No. of Match Box = —————————
                                Vol. of Matchbox

                                    8 × 8 × 8
No. of Match Box = ——————
                                    2 × 2 × 2

                                    8 × 8 × 8
No. of Match Box = ——————
                                           8
                                    
No. of Match Box = 8 × 8 
No. of Match Box = 64
Q. 7 Multiply the following.
(i) 9(y+1)(x+2)
(ii) m(m+2)(m+1)

Sol. (i)
   9(y+1)(x+2)
= 9[(y+1)(x+2)]
= 9[(y(x+2)+1(x+2)]
= 9[xy+2y+1x+2]
= 9xy+18y+9x+18

Sol. (ii)

   m(m+2)(m+1)
= m[(m+2)(m+1)]
= m[(m(m+2)+1(m+2)]
= m[m²+2m+1m+2]
= m[m²+3m+2]
= m³+3m²+2m

Q.8  find the value by applying the suitable identities 
(i) (5x –4y)²
(ii) (7z + 3y)(7z + 3y)
Sol.    
(i) (5x –4y)²
By identity  
(a – b)²  = (a)² – 2.a.b + (b)²
(5x – 4y)² 
 = (5x)² – 2.5x.4y + (4y)²   
 = 25x² – 40xy + 16y²   

(ii) (7z + 3y)(7z + 3y)
By identity  
(a + b)(a + b) = (a + b)²
(a + b)² = (a)² – 2.a.b + (b)²

  (7z + 3y)(7z + 3y)
= (7z + 3y)² 
 = (7z)² + 2.7z.3y + (3y)²   
 = 49x² + 42yz + 9y²   

Q.9 By using the suitable identities find the value of
(956)² –(44)²
Sol.    
(956)² –(44)²
By identity  
(a)² –(b)²  = (a+b)(a–b)
(956)² –(44)² 
 = (956+44)(956–44)         
 = (1000)(912)
 = 912000          
  
Q. 10  The width of the cuboid is 3 cm less than its length and height is 5 cm less than its length, find the volume of the cuboid? 
Sol.
Let the Length of the cuboid (l)= m
then Breadth (b) =  (m–3)    
         Height.   (h) = (m–5)

volume of the cuboid = l×b×h

= m(m – 3)(m – 5)
= m[(m – 3)(m – 5)]
= m[(m(m – 5) –1(m – 5)]
= m[m² – 5m –1m + 5]
= m[m² – 6m + 5]
= m³ – 6m² + 5m

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