Question

Resolve into factors.

a)x4-5x2y2+4y4

Answer 1

Answer:

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

Step-by-step explanation:

Given

$x^{4}$ - 5x²y² + 4$y^{4}$

Consider the factors of the coefficient of the $y^{4}$ term (+ 4) which sum to give the coefficient of the x²y² term (+ 5)

The factors are - 1 and - 4 , thus

$x^{4}$ - 5x²y² + 4$y^{4}$

= (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

$x^{4}$ - 5x²y² + 4$y^{4}$

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