Resolve into factors.

a)x4-5x2y2+4y4

(x - y)(x + y)(x - 2y)(x + 2y)

Step-by-step explanation:

Given

- 5x²y² + 4

Consider the factors of the coefficient of the term (+ 4) which sum to give the coefficient of the x²y² term (+ 5)

The factors are - 1 and - 4 , thus

- 5x²y² + 4

= (x² - y²)(x² - 4y²)

Both of these factors are differences of squares which factor in general as

a² - b² = (a - b)(a + b) , so

x² - y² = (x - y)(x + y)

x² - 4y²

= x² - (2y)² = (x - 2y)(x + 2y)

Hence

- 5x²y² + 4

= (x - y)(x + y)(x - 2y)(x + 2y) ← in factor form

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2