Question

factorize a^12x^4-a^4x^12

Answer 1

a¹².y⁴ - a⁴.y¹²

you can write a¹² = a⁴.a^8
again, y¹² = y⁴.y^8

now use this,

= a⁴.a^8.y⁴ - a⁴.y⁴.y^8
you see that a⁴.y⁴ are common terms in both so,

= a⁴.y⁴( a^8 - y^8)
[ use,formula , x² - y² = (x - y)(x + y) ]

= a⁴.y⁴(a⁴ - y⁴)(a⁴ + y⁴)

=a⁴.y⁴(a² - y²)(a² + y²)(a⁴+y⁴)

=a⁴.y⁴(a - y)(a+ y)(a²+y²)(a⁴ + y⁴)

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Answer 2

a^12x^4-a^4x^12
a^4x^4(a^8-x^8)