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Factors of a³ - b³

Factorize the...

Question

Factorize the following expression:

$x^{5} - 16 x^{3}$

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Solution

Given: $x^{5} - 16 x^{3}$

$∴ x^{5} - 16 x^{3}$
$= x^{3} (x^{2} - 16)$
$= x^{3} (x^{2} - 4^{2})$

Using the formula , $(a^{2} - b^{2}) = (a - b) (a + b)$

$= x^{3} (x + 4) (x - 4)$

Hence, $x^{5} - 16 x^{3} = x^{3} (x + 4) (x - 4)$

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Similar questions

16 x^{3}, - 4 x^{2}, 32 x

Find the common factors of the terms

(i) $12 x, 36$

(ii) $2 y, 22 x y$

(iii) $14 p q, 28 p^{2} q^{2}$

(iv) $2 x, 3 x^{2}, 4$

(v) $6 a b c, 24 a b^{2}, 12 a^{2} b$

(vi) $16 x^{3}, - 4 x^{2}, 32 x$

(vii) $10 p q, 20 q r, 30 r p$

(viii) $3 x^{2} y^{3}, 10 x^{3} y^{2}, 6 x^{2} y^{2} z$

12 x, 36

2 y, 22 x y

14 p q, 28 p^{2} q^{2}

2 x, 3 x^{2}, 4

6 a b c, 24 a b^{2}, 12 a^{2} b

16 x^{3}, - 4 x^{2}, 32 x

10 p q, 20 q r, 30 r p

3 x^{2} y^{3}, 10 x^{3} y^{2}, 6 x^{2} y^{2} z

16 x^{3} - 36 x

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