Question

Challenge!
Factorise completely: 256xl7y2 - xyz.​

Answer 1

Step-by-step explanation:

256x^17y^2 - xy^2

=xy²(256x^16 - 1)

=xy²[(16x^8)² - (1)²]

=xy²[(16x^8 +1)(16x^8 - 1)]

=xy²(16x^8 + 1)[(4x⁴)² - (1)²]

=xy²(16x^8 + 1)(4x⁴ + 1)(4x⁴ - 1)

=xy²(16x^8 + 1)(4x⁴ + 1)[(2x)² - (1)²]

=xy²(16x^8 + 1)(4x⁴ + 1)(2x + 1)(2x - 1)

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Concept Used:

a² - b² =(a + b)(a - b)

and

(a^m)^n = a^(mn)

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