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Multiplication of Any Polynomial

1 y 3 -27 2 ...

Question

(1) $y^{3} - 27$
(2) $x^{3} - {64 y}^{3}$
(3) ${27 m}^{3} - {216 n}^{3}$
(4) ${8 p}^{3} - \frac{27}{p^{3}}$
(5) ${343 a}^{3} - {512 b}^{3}$
(6) ${64 x}^{3} - {729 y}^{3}$

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Solution

$\begin{matrix} (1) y^{3} - {(3)}^{3} = (y - 3) (y^{2} + 3 y + 9) (2) x^{3} - {(4 y)}^{3} = (x - 4 y) (x^{2} + 4 x y + 16 y^{2}) (3) {(3 m)}^{2} - {(6 n)}^{3} = (3 m - 6 n) (9 m^{2} + 18 m n + 36 n^{2}) (4) {(2 p)}^{3} - {(\frac{3}{p})}^{3} = (2 p - \frac{3}{p}) (4 p^{2} + \frac{6 p}{p} + \frac{9}{p^{2}}) = (4 p^{2} + 6 + \frac{9}{p^{2}}) (5) {(7 a)}^{3} - {(8 b)}^{3} = (7 a - 8 b) (49 a^{2} + 56 a b + 64 b^{2}) (6) {(4 x)}^{3} - {(9 y)}^{3} = (4 x - 9 y) (16 x^{2} + 36 x y + 81 y^{2}) \end{matrix}$

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Similar questions

Q. Factorize
i)

27 m^{3} - 216 n^{3}

343 a^{3} - 512 b^{3}

Q. Factorise:
(1) y³− 27
(2) x³− 64y³
(3) 27m³− 216n³
(4) 125y³− 1
(5) 8p³−

\frac{27}{p^{3}}

(6) 343a³ − 512b³
(7) 64x³− 729y³
(8) 16a³−

\frac{128}{b^{3}}

27 m^{3} - 216 n^{3}

64 x^{3} - 729 y^{3}

64 x^{3} - 729 y^{3}

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