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प्रश्न
Factorize the following expressions:
x3 + 6x2 +12x +16
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उत्तर
= x3 + 6x2 +12x + 8 + 8
= x3 + 3 × x2 × 2 + 3 × x × 22 + 23 + 8
= ( x = 2)3 + 8 [ ∵ a3 + 3a2b + 3ab2 + b3 = (a + b)3]
= ( x + 2)3 + 23
= ( x + 2 + 2)(( x + 2)2 - 2 ( x + 2) + 22 ) [∵ a3 + b3 = (a + b)(a2 - ab + b2 ) ]
= ( x + 4)(x2 + 4x + 4 - 2x - 4 + 4) [∵ (a + b)2 = a2 + 2ab + b2]
= ( x + 4)(x2 + 2x + 4)
∴ x3 + 6x2 +12x +16 = ( x + 4)(x2 + 2x + 4)
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