(209*144)^2 + 209*209+ 144*144+ 209*144 = ?

• 905863729
  
  
  (209*144)^2 + (209*209)+(209*144)+(144*144)= S
  let 144 =X and 209 = Y
  then the above equation will be
  (XY)^2 + Y^2 + XY + X^2 = (X+Y)^2 - XY +(XY)^2
  = (X+Y)^2 + XY( XY -1)
  putting values of x and y,
  = (144+209)^2 + 144*209(144*209 - 1)
  = 353^2 + 30096*30095
  =124609 + 905739120
  =905863729
• 11 years agoHelpfull: Yes(18) No(3)
• suppose x=209 and y=144
  
  so (209*144)^2 + 209*209+ 144*144+ 209*144 = (x*y)^2 + x^2 + y^2 + x*y
  =X^2 + 2*x*y + y^2 + (x*y)^2 - x*y
  =(x+y)^2 + (x*y)(x*y - 1)
  =(209 + 144)^2 + (209*144)(209*144 - 1)
  =(353)^2 + (30096)(30095)
  =905863729
• 11 years agoHelpfull: Yes(5) No(0)
• first we solve (209*144)^2+209*209+144*144
  it is a formula (a+b)^2=a^2+b^2+2ab so (209+144)^2
  now it will be (209+144)^2+ 209*144
  =124609+ 30096=154705
  ans:154705
• 11 years agoHelpfull: Yes(1) No(14)
• (209*144)^2 + (209*209+ 144*144+ 209*144 )
  (a+b)^2=a^2+b^2+2ab
  (209*144)^2+(209+144)^2
  905769216+124609=905893825
  ans is 905893825
• 11 years agoHelpfull: Yes(0) No(4)
• calculator is allow na in written exam ????
• 11 years agoHelpfull: Yes(0) No(0)