a^12y^4 - a^4y^12 factorise this equation
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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)
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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