"Factor each polynomial. If a polynomial cannot be..." solved and explained

Marvin Mccormick

Answered question

2021-04-14

Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary:

27 r^{3} - 64 s^{3}

Nathaniel Kramer

Skilled2021-04-16Added 78 answers

Given,

27 r^{3} - 64 s^{3}

On simplification, we get

27 r^{3} - 64 s^{3} = 3^{3} r^{3} - 4^{3} s^{3}

= {(3 r)}^{3} - {(4 s)}^{3}

= (3 r - 4 s) [{(3 r)}^{2} + (3 r) (4 s) + {(4 s)}^{2}] [∵ a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})]

= (3 r - 4 s) (9 r^{2} + 12 r s + 16 s^{2})

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