Question

Factorise :-
a¹² x⁴ - a⁴x¹²​

Answer 1

Solution -

We have,

• a¹²x⁴ - a⁴x¹²

⠀

Factorizing

➝ a⁴x⁴ (a⁸ - x⁸)

➝ a⁴x⁴ {(a⁴)² - (x⁴)²}

➝ a⁴x⁴ {(a⁴ + x⁴) (a⁴ - x⁴)}

➝ a⁴x⁴ (a⁴ + x⁴) {(a²)² - (x²)²}

➝ a⁴x⁴ (a⁴ + x⁴) (a² + x²) (a² - x²)

➝ a⁴x⁴ (a⁴ + x⁴) (a² + x²) {(a)² - (x)²}

➝ a⁴x⁴ (a⁴ + x⁴) (a² + x²) (a + x) (a - x)

⠀

Identity used here

• a² - b² = (a + b) (a - b)

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