Question

Factorise:
a) 32x⁴-8y²​

Answer 1

8(2x² - y)(2x² + y)

Explanation:

32
`x^(4)` - 8y² ← factor out 8 from each term

= 8(4
`x^(4)` - y²) ← difference of squares which factors in general as

a² - b² = (a - b)(a + b) , then

4
`x^(4)` - y²

=
`(2x^2)^(2)` - y²

= (2x² - y)(2x² + y)

Thus

32
`x^(4)` - 8y² = 8(2x² - y)(2x² + y)