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WORKSHOP CALCULATION - CITS

EXERCISE 4 : Algebra

Fundamental Algebraic formulae for multiplication and factorization
Algebra is a branch of mathematics which substitutes letters for numbers. An algebraic equation depicts a scale,
what is done on one side of the scale with a number is also done to either side of the scale. Algebra also includes
real numbers, complex numbers, matrices, vectors and much more. The numbers are constants. X, Y, A, B are
the most frequently used letters that specify algebraic problems and equations.
Algebraic equations, simple & simultaneous equations
Here is a list of Algebraic formulas –
• a – b = (a – b)(a + b)
2
2
• (a + b) = a + 2ab + b 2
2
2
• a + b = (a + b) – 2ab
2
2
2
• (a – b) = a – 2ab + b 2
2
2
• (a + b + c) = a + b + c + 2ab + 2bc + 2ca
2
2
2
2
• (a – b – c) = a + b + c – 2ab + 2bc – 2ca
2
2
2
2
• (a + b) = a + 3a b + 3ab + b ; (a + b) = a + b + 3ab(a + b)
3
3
3
3
2
2
2
2
• (a – b) = a – 3a b + 3ab – b = a – b – 3ab(a – b)
2
3
3
3
3
2
3
• If n is a natural number an – b = (a – b)(a + a b+…+ b a + b )
n-2
n
n-1
n-1
n-2
• If n is even (n = 2k), a + b = (a + b)(a – a b +…+ b a – b )
n-2
n-1
n-1
n
n
n-2
• If n is odd (n = 2k + 1), a n + b n = (a + b)(a – a b +a b …- b a + b )
n-2
n-1
n-3 2
n-1
n-2
• (a + b + c + …) = a + b + c + … + 2(ab + ac + bc + ….)
2
2
2
2
• Laws of Exponents (a )(a ) = a m+n ; (ab) = a b ; (a ) = a mn
n
m m
m
m
m n
• Fractional Exponents a = 1 ;
0
Example 1: Find out the value of 5 – 3 2
2
Solution
Using the formula a – b = (a – b)(a + b)
2
2
where a = 5 and b = 3
(a – b)(a + b)
= (5 – 3)(5 + 3)
= 2 × 8 = 16
Example 2:
4 × 4 = ?
3
2
Solution
Using the exponential formula (a )(a ) = a m+n
n
m
where a = 4
4 × 4 = 4 3+2 = 4 = 1024
2
5
3
Quadratic equations and their applications:
The Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax + bx + c
2
=0 where a, b, c, R and a ≠ 0. This is the general form of a quadratic equation where ‘a’ is called the leading
coefficient and ‘c’ is called the absolute term of f (x).
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