Factor this expression completely, then place the factors in the proper location on the grid.
y 3 - 27
you have y^3 - 3^3
remember how to factor the difference of cubes?
a^3-b^3 = (a-b)(a^2+ab+b^2)
To factor the expression y^3 - 27 completely, we can use the difference of cubes formula. The formula states that for any two numbers a and b, the expression a^3 - b^3 can be factored as (a - b)(a^2 + ab + b^2).
In this case, a is y and b is 3. Therefore, we can rewrite the expression as y^3 - 3^3. Now we can apply the difference of cubes formula:
y^3 - 3^3 = (y - 3)(y^2 + y*3 + 3^2)
= (y - 3)(y^2 + 3y + 9)
The expression y^3 - 27 is now fully factored as (y - 3)(y^2 + 3y + 9).
Now, let's place the factors in the proper location on the grid. The factors are (y - 3) and (y^2 + 3y + 9). On the grid, y - 3 goes in the first row, first column, and y^2 + 3y + 9 goes in the first row, second column.