Special Products And Factorization — Formula Sheet

(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

Factorization = reverse process of multiplication

p × q = AC and p + q = B

HCF = product of common factors with highest degree and greatest numerical coefficient

LCM = product of all needed factors with lowest degree and smallest numerical coefficient that are multiples

P/Q

Sum, difference, product, quotient of two rational expressions are rational expressions

Lowest terms when HCF of numerator and denominator is 1

Reciprocal of R/S is S/R

P/Q × R/S = PR/QS

The cube of sum is (a + b)^3 = a^3 + 3ab(a + b) + b^3, and the cube of difference is (a - b)^3 = a^3 - 3ab(a - b) - b^3.

The factorization formulas are (a + b)(a^2 - ab + b^2) = a^3 + b^3 and (a - b)(a^2 + ab + b^2) = a^3 - b^3.