Tag - formulas

FACTORING FORMULAS

Factoring is nothing but breaking down a number or a polynomial into product of its factor which when multiplied together gives the original. Factoring Formula for sum/difference of two nth powers are, PRODUCT FORMULAS a2−b2=(a−b)(a+b)a2−b2=(a−b)(a+b) a3−b3=(a−b)(a2+ab+b2)a3−b3=(a−b)(a2+ab+b2) a3+b3=(a+b)(a2−ab+b2)a3+b3=(a+b)(a2−ab+b2) a4−b4=(a−b)(a+b)(a2−ab+b2)a4−b4=(a−b)(a+b)(a2−ab+b2) a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4)a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4) Product Formulas (a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2 (a−b)2=a2−2ab+b2(a−b)2=a2−2ab+b2 (a+b)3=a3+3a2b+3ab2+b3(a+b)3=a3+3a2b+3ab2+b3 (a−b)3=a3−3a2b+3ab2−b3(a−b)3=a3−3a2b+3ab2−b3 (a+b)4=a4+4a3b+6a2b2+4ab3+b4(a+b)4=a4+4a3b+6a2b2+4ab3+b4 (a−b)4=a4−4a3b+6a2b2−4ab3+b4(a−b)4=a4−4a3b+6a2b2−4ab3+b4 (a+b+c)2=a2+b2+c2+2ab+2ac+2bc(a+b+c)2=a2+b2+c2+2ab+2ac+2bc (a+b+c+…)2=a2+b2+c2+…+2(ab+ac+bc+…)

[Aptitude] Permutation Combination made easy without Formulas

If the following questions make you uncomfortable, then read this article. In how many ways can 5 member committee be formed out of 20 students? Or How many ways can the word “UPSC” be arranged so that “U” is always second from left. In [...]

[Aptitude] PnC: How many Ways to arrange letters of word “RECUPERATE” (Permutation without Formulas)

When you form words using alphabets (or letters), the ‘order’ matters. Three alphabets T,A,C Now you form words: CAT is not same as ACT; both words have different meanings hence order matters. This is a permuation problem. Case 1: All letters are different Case 2: Word [...]

[Aptitude] Compound Interest Rate, Population Growth without Formulas

Introduction Case: City’s population: Growth Case: City’s Population: Decline Case: Bank’s compound interest rate(CI) Case: CI →Finding Nemo Principal Case: Compounding Twice a Year Case: Compounding thrice a year Case: Wine Replacement (Adulteration) Approach 1: Alligiation loop Approach #2: Compound Interest Case: Adulteration→Finding [...]