Online Math Tutoring : Important Formulas – Algebra, Geometry and Trigonometry

Things to Remember: Important Formula for Algebra Math

Important Notes:

  • The square of a number is the number multiplied by itself.
  • A natural number n is a perfect square if n = x2, for all the natural number x.
  • The square of every even number is always even and the square of every odd numbers is always odd.
  • The three consecutive numbers (natural numbers) let’s say a, b and c are called the Pythagorean triplet if
    • c2 = a2+b2
  • If we have a number x, then we can easily find the Pythagorean Triplets by substituting the value in 2x, x2 – 1 and m2 + 1.
  • The square of a natural numbers n is equal to the sum of the first n odd numbers.

For any positive numbers x and y, we have

  • sqrt(ab) = sqrt a x sqrt b
  • sqrt(a/b) = sqrt a / sqrt b
  • sqrt(a+b) (Not equal to sign) sqrt a + sqrt b
  • sqrt(a – b) (Not equal to) sqrt a – sqrt
  • sqrt 2, sqrt 3, sqrt 5, . . . . . . are called the irrationals.
  • The negative of an irrational number is irrational.
  • Zero is called a real number and it has no multiplicative inverse exists.
  • The number e and pi (pi: the value is 3.14 or 22/7) are the irrational numbers.
  • Every Rational number is either rational or irrational.
  • The cube of a number is the line number raised to the power 3 (three).
  • The cube of a negative integer is always negative and positive integer is always positive.
  • The cube of a rational number of x/y is x3/y3.
  • The cube of an even natural number is even and odd natural number is odd.
  • If x be any positive integer, we have 3Sqrt(-x) = -3Sqrt(x).
  • The cube root of a rational number x/y is given by 3Sqrt(x/y) = 3Sqrt(a)/3Sqrt(b).
  • A natural number n is a perfect cube if x = y2, where y is any natural number.
  • The cube root of a given number is that number whose cube is equal to the given number.

Factors and Algebraic Expressions

  • (x + a)(x + b) = x2 + (a + b)x + ab
  • a2 – b2= (a + b)(a – b)
  • (a + b)2 = a2 + 2ab + b2
  • (a – b)2 = a2 – 2ab + b2
  • (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca)
  • (a + b)3 = a3 + b3 + 3ab(a + b)
  • (a – b)3 = a3 – b3 – 3ab(a – b)
  • a3 + b3= (a + b)3 – 3ab(a + b)
  • a3 + b3= (a + b)(a2 – ab + b2)
  • a3 – b3= (a – b)3 + 3ab(a – b)
  • a3 – b3= (a – b)(a2 + ab + b2)
  • a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 -ab – bc – ca)
  • If a + b + c = 0, then a3 + b3 + c3 = 3abc
  • If (a2 + b2 + c2 – ab – bc – ca) = 0, then a3 + b3 + c3 = 3abc.

Factors and Algebraic Expressions

  • Degree of any constant is Zero.
  • The combination of constants and variables connected by +, -, x and / is called the algebraic expressions.
  • A polynomial is called a monomial (having 1 term). binomial (having 2 terms) or trinomial (having 3 terms)
  • Any terms with the same variable and the same exponent are called the like terms.
  • Dividend is the product of Divisor and Quotient and add the Remainder.
  • The degree of the remainder is always less than that of the divisor.
  • An equation is the statement of equality of two algebraic expressions involving one or more unknown quantities.
  • An equation involving only linear polynomials is called a linear equation.
  • The equation, some of the quantity may be added or subtracted from both side of an equation without changing the equality.
  • In the equation, both sides of the equation may be multiplied or divided by the same non-zero number (a number whose denominator part is not zero) without changing the equality.
  • When we solve the equation, we can easily transpose a term from one side to the other side after changing its sign.
  • If (ax + b)/(cx + d) = m/n then n(ax + b) = m(cx + d). This process is called the cross multiplication.