Problem on factorization

factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained. However, factors are not needed to divide evenly because they are still divisible by any number. For example, technically 3 and 8/3 are factors of 8. But, when factoring for tests teachers are looking for the even divisibility of the numbers.

Question:-

factorise m⁸-n⁸

Answer:-

(m⁸-n⁸)

=(m⁴²)-(n⁴²)

=[m⁴+n⁴][m⁴-n⁴]

=[m⁴+n⁴][(m²)²-(n²)²]

=[m⁴+n⁴][m²+n²][m²-n²]

=[m⁴+n⁴][m²+n²][m+n][m-n]


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