# Algebraic Formulas (Special Products)

In Algebra, there are certain products which occur very frequently. By becoming familiar with them, a lot of time can be saved as in those products, multiplication is performed without actually writing down all the steps. Such products are called special products.

$$(a + b)^2 = a^2 + 2ab + b^2$$

$$(a - b)^2 = a^2 - 2ab + b^2$$

$$(a + b)(a - b) = a^2 - b^2$$

$$(x + a)(x + b) = x^2 + (a + b)x + ab$$

$$(ax + b)(cx + d) = acx^2 + (ad + bc)x + bd$$

$$(a + b)^3 = a^3 + 3ab(a + b) + b^3$$

$$(a - b)^3 = a^3 - 3ab(a - b) - b^3$$

$$(a + b)(a^2 - ab + b^2) = a^3 + b^3$$

$$(a - b)(a^2 + ab + b^2) = a^3 - b^3$$

Deductions

$$(a + b)^2 + (a - b)^2 = 2(a^2 + b^2)$$

$$(a + b)2 - (a - b)^2 = 4ab$$

Numerical calculations can be performed more conveniently with the help of special products, often called algebraic formulae.