Question

How do you factor the expression `125b^3+27`?

Answer 1

`(5b+3)(25b^2-15b+9)`

Explanation:

`"this is a "color(blue)"sum of cubes"`

`"which factors in general as"`

`•color(white)(x)a^3+b^3=(a+b)(a^2-ab+b^2)`

`125b^3=(5b)^3rArra=5b`

`27=(3)^3rArrb=3`

`rArr125b^3+27=(5b+3)((5b)^2-(5bxx3)+3^2)`

`color(white)(raArr125b^3+27)=(5b+3)(25b^2-15b+9)`