Question

Factor this expression completely. 5x^3 + 40y^6

Answer 1

see explanation

Explanation:

Given

5x³ + 40
`y^(6)` ← factor out 5 from each term

= 5(x³ + 8
`y^(6)`)

x³ + 8
`y^(6)` ← is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²)

x³ + 8
`y^(6)`

= x³ + (2y²)³ → a = x and b = 2y²

= (x + 2y²)(x² - 2xy² + 4
`y^(4)`)

Hence

5x³ + 40
`y^(6)`

= 5(x + 2y²)(x² - 2xy² + 4
`y^(4)`) ← in factored form