Question

Factor Completely 192x^3 + 375

Answer 1

`192x^3 + 375 : GCF = 3`


`3( (192x^3)/(3) + (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)`

Answer 2

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)