How do you factor $a^{3} b^{3} - 16 a b^{3}$ $a^3b^3-16ab^3$ ?

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How do you factor $a^{3} b^{3} - 16 a b^{3}$ $a^3b^3-16ab^3$ ?

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Answer 1 · 2016-05-06T09:30:23

$a b^{3} (a - 4) (a + 4)$ $ab^3(a-4)(a+4)$

Explanation:

Looking for common factors in the 2 terms.

from $a^{3} and a we get a$ $a^3" and a we get " a$

from $b^{3} and b^{3} \to b^{3}$ $b^3 and" b^3→ b^3$

$\Rightarrow a^{3} b^{3} - 16 a b^{3} = a b^{3} (a^{2} - 16)$ $rArra^3b^3-16ab^3=ab^3(a^2-16)$

now $a^{2} - 16 is a difference of squares$ $a^2-16" is a" color(blue)" difference of squares"$

and in general factorises as $a^{2} - b^{2} = (a - b) (a + b)$ $a^2-b^2=(a-b)(a+b)$

For $a^{2} - 16, a = a and b = 4 \to (a - 4) (a + 4)$ $a^2-16 , a=a " and " b=4→ (a-4)(a+4)$

$rArrcolor(red)(|bar(ul(color(white)(a/a)color(black)(a^3b^3-16ab^3=ab^3(a-4)(a+4))color(white)(a/a)|))$

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How do you factor $a^{3} b^{3} - 16 a b^{3}$ $a^3b^3-16ab^3$ ?

1 Answer

Explanation:

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How do you factor $a^{3} b^{3} - 16 a b^{3}$ $a^3b^3-16ab^3$ ?