OpenStudy (anonymous):

4 years ago
OpenStudy (anonymous):

Factor this expression completely, then place the factors in the proper location on the grid. y^3 - 27

4 years ago
OpenStudy (studygurl14):

So, I'm guessing you don't know how to factor, right?

4 years ago
OpenStudy (anonymous):

I know some of it but there are a few questions I cannot seem to get and I don't know what I'm doing wrong.

4 years ago
OpenStudy (mathstudent55):

$$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$

4 years ago
OpenStudy (mathstudent55):

Are you familiar with the factoring of the difference of two cubes shown above?

4 years ago
OpenStudy (mathstudent55):

In your case, a = y, and b = 3. $$y^3 - 3^3$$

4 years ago
OpenStudy (anonymous):

No. I know the simpler factoring but that formula confuses me and I cannot figure out how to plug it in.

4 years ago
OpenStudy (mathstudent55):

Look at the right side, where you have $$(a - b)(a^2 + ab + b^2)$$. See it? Plug in y for a and 3 for b. That's all there is to it. Then since you are actually dealing with a number, you can rewrite $$3^2$$ as 9.

4 years ago
OpenStudy (anonymous):

Where did you get the 3 at?

4 years ago
OpenStudy (mathstudent55):

Here I'm doing it color coded. $$\color{red}a^3 - \color{green}b^3 = (\color{red}a - \color{green}b)\color{red}(\color{red}a^2 + \color{red}a\color{green}b + \color{green}b^2)$$

4 years ago
OpenStudy (mathstudent55):

Your problem is $$y^3 - 27$$, right? If this is the difference of two cubes, I can see that y cubed is a cube. Obviously, y cubed is the cube of y. Is 27 a cube? If so, it is the cube of what?

4 years ago
OpenStudy (anonymous):

Oh okay so because 27 is the cube of 3, that's where you got the 3 from?

4 years ago
OpenStudy (mathstudent55):

Exactly. Now we can rewrite it as the the difference of 2 cubes by replacing 27 with $$3^3$$.

4 years ago
OpenStudy (anonymous):

Okay so the answer would be (y-3)(y^2+3y+9)?

4 years ago
OpenStudy (mathstudent55):

Here is your problem showing the cubes clearly, and color coded to match the formula above. $$\color{red}y^3 - \color{green}3^3$$ Now we replace $$\color{red}a$$ with $$\color{red}y$$, and $$\color{green}b$$ with $$\color{green}3$$. $$\color{red}y^3 - \color{green}3^3 = (\color{red}y - \color{green}3)\color{red}(\color{red}y^2 + \color{red}y\color{green}\cdot 3 + \color{green}3^2)$$

4 years ago
OpenStudy (anonymous):

Can you help me with another?

4 years ago
OpenStudy (mathstudent55):

The final answer is: $$y^3 - 27 = (y - 3) (y^2 + 3y + 9)$$ You are correct.

4 years ago
OpenStudy (mathstudent55):

Sure. Can you pls start a new post. I'll look for it.

4 years ago
OpenStudy (anonymous):

Sure!

4 years ago