Question

factorise both the parts

Answer 1

i) x^6-y^6
= (x^3)^2 - (y^3)^2

Using identity a^2 -b^2 =(a+b)(a-b)

=(x^3+y^3)(x^3-y^3)



Using identity a^3 + b^3 = (a + b)(a^2 – ab + b^2)
And
a^3 – b^3 = (a – b)(a^2 + ab + b^2)



= (x+y)(x^2 -xy+ y^2) (x-y)(x^2 +xy +y^2)



So, x^6- y^6 would be factorised as

= (x+y) (x-y) (x^2 -xy+ y^2) (x^2 +xy +y^2)



ii) x^12 -y^12
= (x^6)^2 - (y^6)^2

Using the indentity a^2 -b^2 =( a+b)(a-b)


= (x^6 +y^6) (x^6-y^6)
= (x^6 +y^6){( x^3)^2 -(y^3)^2}

Using identity a^2 -b^2 =(a+b)(a-b)

=(x^6+y^6) (x^3+y^3)(x^3-y^3)


Using identity a^3 + b^3 = (a + b)(a^2 – ab + b^2)
And
a^3 – b^3 = (a – b)(a^2 + ab + b^2)



=(x^6+y^6) (x+y)(x^2 -xy+ y^2) (x-y)(x^2 +xy +y^2)



So, x^12- y^12 would be factorised as

= (x^6+y^6) (x+y) (x-y) (x^2 -xy+ y^2) (x^2 +xy +y^2)