Question

Factor Completely 192x^3 + 375

Answer 1

192$x^{3}$+375

Factor out common term 3:
3(64$x^{3}$+125)

Next, factor 64$x^{3}$+125:
Apply the sum of cubes rule:
$x^{3}$+$y^{3}$=(x+y)($x^{2}$-xy+$y^{2}$)

64$x^{3}$+125 = (4x+5)($4^{2}$$x^{2}$-4*5x+$5^{2}$)

Refine to receive the simplified answer:
3(4x+5)($4^{2}$$x^{2}$-4*5x+$5^{2}$)
3(4x+5)(16$x^{2}$-20x+25)

Answer 2

$192x^3 + 375 : GCF = 3$ 

$3( \dfrac{192x^3}{3} + \dfrac{375}{3} )$ 

$3(64x^3+125)$ 

$3((4x)^3+5^3)$ 

$\text{Use Sum of Cubes:} \ {a}^{3}+{b}^{3}=(a+b)({a}^{2}-ab+{b}^{2})$

$3((4x+5)((4x)^2-(4x)(5)+5^2))$ 

$\text{Use Multiplication Distributive Property:} {(xy)}^{a}={x}^{a}{y}^{a}(xy)$ 

$3(4x+5)(4^2x^2-4x*5+5^2)$ 

$3(4x+5)(16x^2-4x*5+5^2)$ 

$3(4x+5)(16x^2-4x*5+25)$ 

$3(4x+5)(16x^2-20x+25)$