Question

Factorise the following.​

Answer 1

Answer:

x²(9x– 11)(9x + 11)

Step-by-step explanation:

81x⁴ – 121x²

The expression can be factorised as follow:

81x⁴ – 121x²

x² is common to both term. Thus:

81x⁴ – 121x² = x²(81x² – 121)

Recall:

81 = 9²

121 = 11²

Therefore,

x²(81x² – 121) = x²(9²x² – 11²)

= x²[(9x)² – 11²]

Difference of two squares

x²(9x– 11)(9x + 11)

Therefore,

81x⁴ – 121x² = x²(9x– 11)(9x + 11)