Respuesta :

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192[tex] x^{3} [/tex]+375

Factor out common term 3:
3(64[tex] x^{3} [/tex]+125)

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

64[tex] x^{3} [/tex]+125 = (4x+5)([tex] 4^{2} [/tex][tex] x^{2} [/tex]-4*5x+[tex] 5^{2} [/tex])

Refine to receive the simplified answer:
3(4x+5)([tex] 4^{2} [/tex][tex] x^{2} [/tex]-4*5x+[tex] 5^{2} [/tex])
3(4x+5)(16[tex] x^{2} [/tex]-20x+25)
[tex]192x^3 + 375 : GCF = 3 [/tex] 

[tex]3( \dfrac{192x^3}{3} + \dfrac{375}{3} )[/tex] 

[tex]3(64x^3+125)[/tex] 

[tex]3((4x)^3+5^3)[/tex] 

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

[tex]3((4x+5)((4x)^2-(4x)(5)+5^2))[/tex] 

[tex]\text{Use Multiplication Distributive Property:} {(xy)}^{a}={x}^{a}{y}^{a}(xy) [/tex] 

[tex]3(4x+5)(4^2x^2-4x*5+5^2)[/tex] 

[tex]3(4x+5)(16x^2-4x*5+5^2)[/tex] 

[tex]3(4x+5)(16x^2-4x*5+25)[/tex] 

[tex]3(4x+5)(16x^2-20x+25)[/tex] 

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