Question

How do you factor `64+27t^3`?

Answer 1

`(4 + 3t)(16 - 12t + 9t^2 )`

Explanation:

This is a `color(blue)" sum of 2 cubes " " and factors as follows "`

`a^3 + b^3 = color(red)(|bar(ul(color(white)(a/a)color(black)((a+b)(a^2-ab+b^2)color(white)(a/a)|)))`

For `64 + 27t^3 , " a = 4" and b = 3t "`

substituting these values into the factored form.

`rArr 64 + 27t^3 = (4 + 3t)(16 - 12t + 9t^2)`