Basic Algebra
(a + b)^{2}= a^{2} + 2ab + b^{2} 
(a – b)^{2} = a^{2} – 2ab + b^{2} 
a^{2} – b^{2} = (a + b)(a – b) 
a^{2} + b^{2} = (a + b)^{2} – 2ab or (a – b)^{2} + 2ab 
(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc +ac) or a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca 
(a – b – c)^{2} = a^{2} + b^{2} + c^{2} – 2(ab – bc +ac) or a^{2} + b^{2} + c^{2} – 2ab + 2bc – 2ca 
(a + b)^{3} = a^{3} + b^{3} + 3ab(a + b) or a^{3} + 3a^{2}b + 3ab^{2} + b^{3} 
(a – b)^{3} = a^{3} – b^{3} – 3ab(a – b) or a^{3} – 3a^{2}b + 3ab^{2} – b^{3} 
a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2}) 
a^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2}) 
a^{4} – b^{4} = (a^{2} – b^{2})(a^{2} + b^{2}) or (a – b)(a + b)(a^{2} + b^{2}) 
a^{5} – b^{5} = (a – b)(a^{4} + a^{3}b + a^{2}b^{2} + ab^{3} + b^{4}) 
a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b + a^{n3}b^{2} … – ab^{n2} + b^{n1}) 
Indices
p^{n} = p.p.p…….n times 
p^{n}⋅ p^{m} = p^{m+n} 
p^{n} ⋅ q^{n} = (p ⋅ q)^{n} 
p^{m}/ p^{n} = x^{mn} 
p^{n} / q^{n} = (p / q)^{n} 
(p^{n})^{m} = p^{n⋅m} 
_{p}n^{m} = _{p}(n^{m}) 
p^{n} = 1 / p^{n} 
a^{0} = 1 where a ∈ R , a!=0 
Mathematical Properties
Commutative Property of Addition : a + b = b + a 
Commutative Property of Multiplication : a x b = b x a 
Associative Property of Addition : a + (b + c) = (a + b) + c 
Associative Property of Multiplication : a x (b x c) = (a x b) x c 
Additive Identity Property : a + 0 = a 
Multiplicative Identity Property : a x 1 = a 
Additive Inverse Property : a + ( – a ) = 0 
Multiplicative Inverse Property : a ( 1/a ) = 1 
Zero Property of Multiplication : a x 0 = 0 
Mensuration
Perimeter 

Circumference 

Area 

Surface Area 

Volume 

Pythagoras Theorem 

Distance Formula 

Slope of a line 

Mid Point Formula 

Slopeintercept form of the equation of a line 

Quadratic formula 

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اللہ تعالی عزوجل یہ علمی ویب سائیٹ بنانے والے انکے والدین بیوی بچوں کے علم عُمر عمل میں بے حساب اضافہ فرمائیں اور ان سب کا خاتمہ ایمان پر فرمائیں آمین ثم آمین یارب العالمین بجاہ النبی الامین صلی اللہ تعالی علیہ والہ واصحابہ وبارک وسلم
Ameen. Thank You. Muhammad Zia
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