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Grade 8 - Mathematics
7.50 Formulas Review

  1. Algebraic expressions in which the variables involved have only non-negative integral exponents are called polynomials.
  2. A polynomial that involves only one variable is called a polynomial in one variable.
  3. The highest exponent of the variable in various terms of a polynomial in one variable is called its degree.
  4. A constant is a polynomial of degree zero.
  5. The standard form of a polynomial in one variable is that in which the terms of the polynomial are written in the decreasing order of the exponents of the variable.
  6. The coefficient in the quotient of two monomials is equal to the quotient of their coefficients.
  7. The variable part in the quotient of two monomials is equal to the quotient of the variable parts in the given monomials.
  8. If on dividing a polynomial (dividend) by a polynomial (divisor), a zero remainder is obtained, then the divisor is a factor of the dividend. In such cases, quotient is also a factor of the dividend. Further,
    Dividend = Divisor Quotient
  9. In general,
    Dividend = Divisor Quotient + Remainder
  10. The degree of the remainder is always less than the degree of the divisor.
  11. Before performing long division, the divisor and the dividend must be written in the standard form.
  12. While performing long division, like terms are written one below the other, leaving gaps wherever necessary.

Important Formulas

1. (a+b)2 = a2+2ab+b2

2. (a-b)2 = a2-2ab+b2

3. (a+b)(a-b) = a2-b2

4. (a+b)(a2-ab+b2) = a3+b3

5. (a-b)(a2+ab+b2) = a3-b3

6. (a+b)3 = a3+3a2b+3ab2+b3

7. (a-b)3 = a3-3a2b+3ab2-b3

8. (a+b+c)2 = a2+b2+c2+2ab+2bc+2ac

9. (a+b+c) (a2+b2+c2-ab-bc-ca)= a3+b3+c3-3abc

10. (x+a)(x+b) = x2+x(a+b)+a.b

11. (ax+b)(cx+d) = acx2+x(ad+bc)+b.d

12. (x+a)(x+b)(x+c) = x3+x2(a+b+c)+x(ab+bc+ca)+abc

Directions: Memorize the formulas and write all the formulas on a sheet of paper.