Question

Factorise 2a⁷+128a

Answer 1

2a⁷ - 128a

= 2a • (a⁶ - 64)

Factoring: a⁶ - 64
A difference of two perfect squares, A² - B² can be factored into (A+B) • (A-B)
64 is the square of 8
a⁶ is the square of a³

a⁶ - 64 = (a³ + 8) • (a³ - 8)
= 2a • (a³ + 8) • (a³ - 8)

Factoring: a³ + 8
A sum of two perfect cubes, a³ + b³ can be factored into : (a+b) • (a²-ab+b²)
a³ + 8 = (a + 2) • (a² - 2a + 4)

Factoring: a³- 8
A difference of two perfect cubes, a³ - b³ can be factored into
(a-b) • (a² +ab +b²)

Factorization is :
a³- 8 = (a - 2) • (a² + 2a + 4) so, final result is, 2a⁷ - 128a = 2a•(a+2)•(a²-2a+4)•(a-2)•(a²+2a+4) these type of questions are done step wise.