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Factorize: (x + 1)(x + 2)(x + 3)(x + 6) - 3x2.

Factorize: (x + 1)(x + 2)(x + 3)(x + 6) - 3x2.

Grade:10

1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
The given question is (x + 1)(x + 2)(x + 3)(x + 6) – 3x2. …... (1)
There is no direct way of approacching this question. However, one of the probable way is that you may split the terms in two groups like:
We first take (x+1)(x+6) and then ((x+2)(x+3).
(x + 1)(x + 6) = x2 + 7x + 6 = x2 + 6x + 6 + x …. (2)
(x + 2)(x + 3) = x2 + 5x + 6 = x2 + 6x + 6 - x ….. (3)
Putting the values obtained in (2) and (3) in (1), we get,
(x + 1)(x + 2)(x + 3)(x + 6) – 3x2 = (x2 + 6x + 6 + x) (x2 + 6x + 6 – x) – 3x2
= [(x2 + 6x + 6) + x] [(x2 + 6x + 6) – x] – 3x2
Now using the formula (a+b)(a-b) = a2-b2, we get
[(x2 + 6x + 6) + x] [(x2 + 6x + 6) – x] – 3x2 = (x2 + 6x + 6)2 - x2 – 3x2
= (x2 + 6x + 6)2 - 4x2
Again using the formula (a+b)(a-b) = a2-b2, we get
(x2 + 6x + 6)2 - 4x2 = (x2 + 6x + 6 – 2x) (x2 + 6x + 6 + 2x)
= (x2 + 4x + 6 )(x2 + 8x + 6 ).
Thnaks & Regards
Latika Leekha
askIITians Faculty

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