Chapter 1 Class 10 Real Numbers
Concept wise

Square Formulas

• (a + b) 2 = a 2 + b 2 + 2ab
• (a − b) 2 = a 2 + b 2 − 2ab
• a 2 − b 2 = (a − b) (a + b)
• (x + a) (x + b) = x 2 + (a + b) x + ab
• (a + b + c) 2 = a 2 + b 2 + c 2  + 2ab + 2bc + 2ca
• (a + (−b) + (−c)) 2 = a 2 + (−b) 2  + (−c) 2 + 2a (−b) + 2 (−b) (−c) + 2a (−c)

(a – b – c) 2 = a 2 + b 2 + c 2 − 2ab + 2bc − 2ca

Cube Formulas

• (a + b) 3 = a 3 + b 3 + 3ab(a + b)
• (a − b) 3 = a 3 - b 3 - 3ab(a - b)
• a 3 − b 3 = (a − b) (a 2 + b 2 + ab)
• a 3 + b 3 = (a + b) (a 2 + b 2 − ab)
• (a + b + c) 3 = a 3 + b 3 + c 3 + 3(a + b)(b + c)(c + a)
• a 3 + b 3 + c − 3abc = (a + b + c) (a 2 + b 2 + c 2 − ab − bc − ac)
• If (a + b + c) = 0,
a 3 + b 3 + c 3 = 3abc

Power n Formula

• a n − b n = (a − b) (a n−1 + a n−2  b 1  + a n−3  b 2 + .... + a b n−2  + b n−1  )

Exponent Law

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• √a = a 1/2

• ∛a = a 1/3

• n √a = a 1/n

• a p.  a q = a p + q
• a p / a q  = a p - q
• a p.  b p = (ab) p
• (a p ) q.  = a pq
• a 0 .  = 1
• a –n.  = 1/a n

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