write all the identities of aldebra
Answers
Algebra
(i) Expansions :
(a ± b)²
(a ± b)³
(x ± a) (x ± b)
(ii) Factorisation
a² - b²
a³ ± b³
ax² + bx + c, by splitting the middle term.
(iii) Changing the subject of a formula.
- Concept that each formula is a perfect equation with variables.
- Concept of expressing one variable in terms of another, various operators on terms - transposing the terms squaring or taking square root etc.
(iv) Linear Equations and Simultaneous (Linear) Equations
(a). Solving algebraically (by elimination as well as substitution) and graphically.
(b) Solving simple problems based on these by framing appropriate formulae.
(v) Indices / Exponents
Handling positive, fractional, negative and "zero" indices.
Simplification of expressions involving various exponents
a^m x a^n = a^(m + n) , a^m ÷ a^n = a^(m-n), (a^m)^n = a^(mn) etc, use of laws of exponents.
(vi) Logarithms
(a) Logarithmic form vis - a - vis exponential form: interchanging.
(b) Laws of Logarithms and its use
Expansion of expression with the help of lacws of logarithm
e. g. y = a⁴ × b²/c³
log y = 4 log a + 2 log b - 3 log c etc.
Some Standard Algebraic Identities list are given below:
Identity I: (a + b)^2 = a^2 + 2ab + b^2
Identity II: (a – b)^2 = a^2 – 2ab + b^2
Identity III: a^2 – b^2= (a + b)(a – b)
Identity IV: (x + a)(x + b) = x^2 + (a + b) x + ab
Identity V: (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
Identity VI: (a + b)^3 = a^3 + b^3 + 3ab (a + b)
Identity VII: (a – b)^3 = a^3 –b^3–3ab (a – b)
Identity VIII: a^3 + b^3 + c^3 – 3abc = (a + b + c)(a^2 + b^2 + c^2 – ab – bc – ca)
Answer:
Algebraic identities:
★ (a + b)² = a² + b² + 2ab
★ (a - b)² = a² + b² - 2ab
★ (a + b + c)² = a² + b² + c² + 2(ab + bc + ac)
★ (a² - b²) = (a + b)(a - b)
★ (a + b)³ = a³ + b³ + 3ab(a + b)
★ (a - b)³ = a³ - b³ - 3ab(a - b)
★ a³ + b³ = (a + b)(a² + b² - ab)
★ a³ - b³ = (a - b)(a² + b² + ab)
★ a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ac)
★ if (a + b + c) = 0 then, a³ + b³ + c³ = 3abc