Question

Factorise :
${x}^{8} - {y}^{8}$
by splitting of middle terms

Answer 1

Given Equation is x^8 - y^8

= > (x^4)^2 - (y^4)^2

We know that a^2 - b^2 = (a + b)(a - b)

= > (x^4 + y^4)(x^4 - y^4)

= > (x^4 + y^4)((x^2)^2 - (y^2)^2))

= > (x^4 + y^4)((x^2 + y^2)(x^2 - y^2))

= > (x^4 + y^4)(x^2 + y^2)(x + y)(x - y).


Hope this helps!

Answer 2

(x^8) - (y^8)

=> (x⁴)² - (y⁴)²

-------------------
By formula,
a²-b² = (a+b) (a-b)
----------------------

=> (x⁴)² - (y⁴)²

=> (x⁴ + y⁴) (x⁴ - y⁴)

=> (x⁴ + y⁴) [ (x²)² - (y²)²]

=> (x⁴ + y⁴) [(x² + y²) (x²-y²) ]

=> (x⁴ + y⁴) (x² + y²) (x + y) (x - y)



I hope this will help you


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