Question

Factorise: a⁸+a⁴b⁴+b⁸
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Answer 1

Answer:

(a^4+b^4) ^2(final answer)

Step-by-step explanation:

= (a^4) ^2+a^4b^4+(b^4) ^2

=(a^4+b^4)^2

Answer 2

Answer:a⁸ + a⁴b⁴ + b⁸

= (a⁴)² – 2a⁴b⁴ + (b⁴)² + 3a⁴b⁴ ←←← Complete the square

= (a⁴ – b⁴)² + (a²b²√3)² ←←← Since x²+2xy+y²=(x+y)²

= ( a⁴– b⁴ )( a⁴+ b⁴) + (a²b²√3)² ←←← Since x²–y²=(x–y)(x+y)

= (a²)² – (b²)²( a⁴+ b⁴) + (a²b²√3)²

=(a²–b²)(a²+b²)( a⁴+ b⁴) + (a²b²√3)²

=(a–b)(a+b)(a²+b²)( a⁴+ b⁴) + (a²b²√3)²