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(x+1)(x+2)(x+3)(x+6)-3x 2 (x+1)(x+1+1)(x+3)(x+3+3)-3x 2 [(x+1) 2 +(x+1)] [ (x+3) 2 +3(x+3)]-3x 2 (x+1) 2 (x+3) 2 +3 (x+1) 2 (x+3) + (x+3) 2 (x+1) + 3 (x+1) (x+3) - 3x 2 (x+1) 2 (x+3) 2 +2 (x+1) (x+3)(2x+3) + 3 (x+1) (x+3) - 3x 2 (x+1) 2 (x+3) 2 +2 (x+1) (x+3)(2x+3) + (2x+3) 2 - (2x+3) 2 - 4 x 2 i didnt get the last and second last step plzz xplain

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


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


(x+1)2(x+3)+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

Grade:10

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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

now  simplify last 3 term it will become -4x2

[(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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Badiuddin

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