Factorise each of the following algebraic expressions completely,

(a) 2k-6k2 + 4k3

(b) 2ax - 4ay + 3bx - 6by

see explanation

Step-by-step explanation:

(a)

Given

2k - 6k² + 4k³ ← factor out 2k from each term

= 2k (1 - 3k + 2k²)

To factor the quadratic

Consider the factors of the product of the constant term (1) and the coefficient of the k² term ( + 2) which sum to give the coefficient of the k - term ( - 3)

The factors are - 1 and - 2

Use these factors to split the k - term

1 - k - 2k + 2k² (factor the first/second and third/fourth terms)

1 (1 - k) - 2k (1 - k) ← factor out (1 - k) from each term

= (1 - k) (1 - 2k)

1 - 3k + 2k² = (1 - k) (1 - 2k) and

2k - 6k² + 4k³ = 2k (1 - k) (1 - 2k)

(b)

Given

2ax - 4ay + 3bx - 6by (factor the first/second and third/fourth terms)

= 2a (x - 2y) + 3b (x - 2y) ← factor out (x - 2y) from each term

= (x - 2y) (2a + 3b)