Question

Factorise: a^12 x^4 – a^4 x^12.

Answer 1

Step-by-step explanation:

Given:-

a^12 x^4 – a^4 x^12.

To find:-

Factorise: a^12 x^4 – a^4 x^12.

Solution:-

Given expression is a^12 x^4 – a^4 x^12

=>(a^4×a^8×x^4)-(a^4×x^4×x^8)

=>a^4×x^4(a^8-x^8)

=>a^4 x^4[(a^4)^2-(x^4)^2]

=>a^4 x^4[(a^4+x^4)(a^4-x^4)]

=>a^4 x^4[(a^4+x^4){(a^2)^2-(x^2)^2}]

=>a^4 x^4[(a^4+x^4)(a^2+x^2)(a^2-x^2)]

=>a^4 x^4[(a^4+x^4)(a^2+x^2)(a+x)(a-x)]

Answer:-

Factorization of expression a^12 x^4 – a^4 x^12

=a^4 x^4 (a+x)(a-x)(a^2+x^2)(a^4+x^4)

Used formula:-

• (a+b)(a-b)=a^2-b^2