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Here, 1st expression = 9x2 - 4y2 - 8yz - 4z2                         = (3x)2 - (4y2 + 8yz + 4z2)                     .....

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1st expression = 4x3 (x-3) (x+2)                          = 2 ⨉ 2  ⨉ x  ⨉ x  ⨉ x (x -3) (x + 2) 2nd expression = 6x2 (x+2) (x+3)     .....

Here,  First expression = (x+2) (x+3),  Second expression = (x+3) (x-2),  Third expression = (x-2) (x-3). Therefore,     LCM = Common factors ⨉ remaining factors         .....

Here,  First expression = (a-3) (a-4) ,  Second expression = (a-4) (a-5),   Third expression = (a-5) (a-3) ∴ LCM = Common facors ⨉ remaining factors             .....

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First expression = a2 +2ab+ b2 -c2  = ( a + b )2 - c2 = ( a + b - c ) ( a + b + c ) Second expression =  b2 +2bc + c2 -a2  = ( b + c )2 - a2 = ( b + c - a ) ( b + c + a )  = ( b + c - a ) ( a + b + .....

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 We know that: a3 + b3 = (a + b) (a2 + ab + .....

First expression : 4x4 + 16x3- 20x2 = 4x2 ( x2 + 4x - 5)  = 4x2 ( x2 + 5x - x - 5)    = 4x2 { x ( x + 5 ) - 1 ( x + 5 )} = 4x2 ( x - 1 ) ( x + 5 ) = 4x.x  ( x - 1 ) ( x + 5 .....

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Here, First expression = ( a + b)2 - 4ab                           = a2 + 2ab + b2 - 4ab                       .....

First expression : x4 - y4  = ( x2 )2 - ( y2 )2   = ( x2 - y2 ) ( x2 + y2 )  = ( x + y ) ( x - y )  ( x2 + y2 )  Second expression : x2 - y2 = ( x - y ) ( x + y .....

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First expression =  4x3 - 10x2 +4x,                           = 2x( 2x2 - 5x + 2)                       .....

अनारको बोट कथाको सारांश र बुँदाटिपोट सुन्दर गाउँमा कल्पलता नाम गरेकी आमा बस्थिन् । उनको .....

We have, equations of diameters  x + 2y = 0   ⟹ x = - 2y  -------------i) And  x + y =6  From (i), - 2y + y  = 6   ⟹ y = - 6 Put y = - 6 in eqn    i) x = - 2 ⨉ (-6) = 12 So, centre .....

First expression : x2 - xy = x (x - y)   Second expression =  x3y - xy3  = xy ( x2 - y2) = xy ( x - y ) ( x + y ) HCF = x . ( x - y ) LCM = HCF x remaining factors  = x . y . ( x - y ) . ( x + y .....

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1st expression =  x2 + 2x - 3                          =   x2 + 3x - x - 3                     .....

1st expression = 8a3 - 98a                             = 2a( 4a2 - 49)                         = 2a (2a .....

First expression : 2x3 + 2x2 - 12x = 2x ( x2 + x - 12 ) = 2x ( x2 + 4x - 3x - 12) =2x { x ( x + 4 ) - 3 ( x + 4 ) } = 2x ( x - 3 ) ( x + 4 ) Second expression : 6x3 - 6x2 -72x = 6x ( x2 - x - 12 .....

1st expression = a4 + a2 + 1                          = (a2)2 + 2.a2.1 + 1 - a2    [ .....

Here,   Final SP( SP with VAT) = SP without VAT + VAT% of SP without VAT Which ie required .....

ii)  S.P with Vat = S.P + Vat % of S.P                           = 5085 + 13 % of  5085                         .....