Basic Algebra
(a + b)2= a2 + 2ab + b2 |
(a – b)2 = a2 – 2ab + b2 |
a2 – b2 = (a + b)(a – b) |
a2 + b2 = (a + b)2 – 2ab or (a – b)2 + 2ab |
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc +ac) or a2 + b2 + c2 + 2ab + 2bc + 2ca |
(a – b – c)2 = a2 + b2 + c2 – 2(ab – bc +ac) or a2 + b2 + c2 – 2ab + 2bc – 2ca |
(a + b)3 = a3 + b3 + 3ab(a + b) or a3 + 3a2b + 3ab2 + b3 |
(a – b)3 = a3 – b3 – 3ab(a – b) or a3 – 3a2b + 3ab2 – b3 |
a3 – b3 = (a – b)(a2 + ab + b2) |
a3 + b3 = (a + b)(a2 – ab + b2) |
a4 – b4 = (a2 – b2)(a2 + b2) or (a – b)(a + b)(a2 + b2) |
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4) |
an + bn = (a + b)(an-1 – an-2b + an-3b2 … – abn-2 + bn-1) |
Indices
pn = p.p.p…….n times |
pn⋅ pm = pm+n |
pn ⋅ qn = (p ⋅ q)n |
pm/ pn = xm-n |
pn / qn = (p / q)n |
(pn)m = pn⋅m |
pnm = p(nm) |
p-n = 1 / pn |
a0 = 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 |
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Circumference |
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Area |
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Surface Area |
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Volume |
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Pythagoras Theorem |
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Distance Formula |
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Slope of a line |
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Mid- Point Formula |
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Slope-intercept form of the equation of a line |
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Quadratic formula |
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Plz make one for Physics