Factor this expression completely, then place the factors in the proper location on the grid.
x^3 + 1/8

(x + 0.5) (x² - 0.5x + 0.25)

Step-by-step explanation:

x³ + 1/8

We can rewrite 1/8 as a decimal: 0.125

the cubed root of 0.125 then is 0.5; recalling that 5³ yields 125

Knowing this then, we can factor out our expression

(ax + b) (ax² − abx + b² ) = ax³ + b³, where a and b are coefficients.

If a = 1, and b we found to = 0.5, our expression becomes

(x + 0.5) (x² - 0.5x + 0.25)

We cannot further factor x² - 0.5x + 0.25, so our answer remains

(x + 0.5) (x² - 0.5x + 0.25)

Check via foiling

(x * x²) + (x * -0.5x) + (x * 0.25) + (0.5 * x²) + (0.5 * -0.5x) + (0.5 * 0.25)

x³ - 0.5x² + 0.25x + 0.5x² - 0.25x + 0.125           Combine like terms

x³ + 0.125 = x³ + 1/8

10 * 563.67 = 5636.7

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".