Factorization by identity a3 + b3

Example 1 . Factorize m3 + 343 by using an identity a3 + b3 = (a + b) (a2 – ab + b2) Solution: m3 + 343 Tip : 343 = 73 So, m3 + 343 = m3 + 73 a3 + b3 So, a = m and b = 7. So, we can factorize m3 + 343 using the identity a3 + b3 = (a + b) (a2 – ab + b2) (a + b) (a2 – ab + b2) = (m + 7) (m2 – m x 7 + 72) Substituting a = m and b = 7 = (m + 7) (m2 – 7m + 49) Thus, m3 + 343 = (m + 7) (m2 – 7m + 49) (Ans)

Example 2. Factorize 64m3 + 8n3 by using an identity a3 + b3 = (a + b) (a2 – ab + b2) Solution: 64m3 + 8n3 Tip: 64m3= (4m)3 and 8n3 = (2n)3 So, 64m3 + 8n3 = (4m)3 + (2n)3 a3 + 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)

Try these Factorize the following expression by using an identity a3 + b3 = (a + b) (a2 – ab + b2) : b3 + 125 27f3 + 1000h3