**Algebra formulas** in math can be used for various purposes like factorization, finding percentages, profit – loss, simple interest, HCF & LCM etc. Some of the formulas we use are:

1. For factorization:

(H + K) ^{2} = H^{2} + K^{2} + 2 HK

(H – K) ^{2} = H^{2} + K^{2} – 2 HK

(H + K) ^{3} = H^{3} + K^{3} + 3 HK (H + K)

(H – K) ^{3} = H^{3} – K^{3} – 3 HK (H – K)

H^{3} + K ^{3} = (H + K) (H^{2} + K^{2} – HK)

H^{3} – K ^{3} = (H – K) (H^{2} + K^{2} + HK)

H^{4} + H^{2} K^{2} +K ^{4} = (H^{2} + K^{2} – HK) (H^{2} + K^{2} + HK)

H^{3} + K^{3} + Z^{3} – 3 HKZ = (H + K + Z) (H^{2} + K^{2} + Z^{2 }– HK – KZ – HZ)

If H + K + Z = 0, we can write:

H^{3} + K^{3} + Z^{3} = 3 HKZ

(H + K + Z) ^{2} = H^{2} + K^{2} + Z^{2} + 2 HK + 2 KZ + 2 HZ

2. For finding percentages:

If we need to find percentage decrease then:

p = (100 / (100 + r)) * 100

If we need to find percentage decrease then:

p = (100 / (100 – r)) * 100

In case of finding percentages in population problems:

a. For population increase

p = P (1 + r) /100) * 100

p = P / (1 + r) /100) * 100

b. For population decrease

p = P (1 – r) /100) * 100

p = P / (1 – r) /100) * 100

Similarly, we can have many other formulas for solving algebraic problems.

Next we discuss the **law of definite proportions**, according to which every pure matter at all times will comprise of same elements that are present in the same proportions by atomic weight.

Icse syllabus for class 1 can be downloaded from various websites.