1. Factorization by
identity a3 + b3

2. Example 1 . Factorize m3 + 343 by using an identity a3 + b3 = (a + b) (a2 – ab + b2)
Solution: m Tip : 343 = 73
So, m = m
a b3
So, a = m and b = 7.
So, we can factorize m using the identity a3 + b3 = (a + b) (a2 – ab + b2)
(a + b) (a2 – ab + b2)
= (m + 7) (m2 – m x ) Substituting a = m and b = 7
= (m + 7) (m2 – 7m + 49)
Thus, m = (m + 7) (m2 – 7m + 49) (Ans)

3. Example 2. Factorize 64m3 + 8n3 by using an identity a3 + b3 = (a + b) (a2 – ab + b2)
Solution: 64m3 + 8n Tip: 64m3= (4m)3 and 8n3 = (2n)3
So, 64m3 + 8n3 = (4m) (2n)3
a b3
So, a = 4m and b = 2n.
So, we can factorize 64m3 + 8n3 using the identity a3 + b3 = (a + b) (a2 – ab + b2)
(a + b) (a2 – ab + b2)
= (4m + 2n) ((4m)2 – 4m x 2n + (2n)2) Substituting a = 4m and b = 2n
= (4m + 2n) (16m2 – 8mn + 4n2)
Thus, 64m3 + 8n3 = (4m + 2n) (16m2 – 8mn + 4n2) (Ans)

4. Try these
Factorize the following expression by using an identity a3 + b = (a + b) (a2 – ab + b2) : b
27f3 + 1000h3