(x+1)(x+2)(x+3)(x+6)-3x²

(x+1)(x+1+1)(x+3)(x+3+3)-3x²

[(x+1)² +(x+1)] [(x+3)² +3(x+3)]-3x²

(x+1)²(x+3)² +3(x+1)²(x+3) + (x+3)²(x+1) + 3(x+1)(x+3) - 3x²

(x+1)²(x+3)² +2(x+1)(x+3)(2x+3) + 3(x+1)(x+3) - 3x²

(x+1)²(x+3)² +2(x+1)(x+3)(2x+3) +(2x+3)² -(2x+3)² - 4x²

^{i didnt get the last and second last step plzz xplain}

Dear ajinkya

(x+1)(x+2)(x+3)(x+6)-3x²

(x+1)(x+1+1)(x+3)(x+3+3)-3x²

[(x+1)² +(x+1)] [(x+3)² +3(x+3)]-3x²

(x+1)²(x+3)²  +3(x+1)²(x+3) + (x+3)²(x+1)  + 3(x+1)(x+3)  - 3x²

here i have taken common (x+1)(x+3)  from the second and third term  (x+1)(x+3)[3(x+1) +(x+3)] = 2(x+1)(x+3)(2x+3)

(x+1)²(x+3)²  +2(x+1)(x+3)(2x+3) + 3(x+1)(x+3)  - 3x²

now i have added and subtracted (2x+3)²  to make perfect square [(x+1)(x+3) +(2x+3)]²

(x+1)²(x+3)²  +2(x+1)(x+3)(2x+3) +(2x+3)² -(2x+3)² +3(x+1)(x+3)- 3x²

[(x+1)(x+3)  +(2x+3)]² - 4x²

[(x+1)(x+3)  +(2x+3) - 2x][(x+1)(x+3)  +(2x+3) + 2x]

[x²+4x+6][x²+8x+6]

[x²+4x+6][x+4+√10][x+4-√10]

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