- Thread starter
- #1
You can think of it this way. Let $a=-\frac{5}{3}$ and $b=\frac{2}{3}$.(- 5x/3 + 2/3) (- 5x/3 + 2/3)
If the above example was;
(-5x + 2) (-5x + 2) = 25x^2 - 10x - 10x + 4 =
25x^2 - 20x + 4
The problem is I don't know how to deal with the denominators in this form?
Anyone help
The shortcuts Chris L T521 mentioned are awesome but if you don't see how they work then this is the much slower way but the method always works with these problems.(- 5x/3 + 2/3) (- 5x/3 + 2/3)
If the above example was;
(-5x + 2) (-5x + 2) = 25x^2 - 10x - 10x + 4 =
25x^2 - 20x + 4
The problem is I don't know how to deal with the denominators in this form?
Anyone help
I have followed through all the above and can see what you have done with the denominator 3, where you have ended up with my original solution, but I didn't know what to do with the denominators.You can think of it this way. Let $a=-\frac{5}{3}$ and $b=\frac{2}{3}$.
Then
\[\left(-\frac{5}{3}x+\frac{2}{3}\right)\left(-\frac{5}{3}x+\frac{2}{3}\right)=(ax+b)(ax+b)=a^2x^2+2abx+b^2\]
Now substitute in the values for a and b to get the answer.
Another way to do this would be to notice that
\[\left(-\frac{5}{3}x+\frac{2}{3}\right)\left(-\frac{5}{3}x+\frac{2}{3}\right)=\frac{1}{3}(-5x+2)\cdot\frac{1}{3}(-5x+2)=\frac{1}{9}(-5x+2)(-5x+2)\]
Thus, the answer would be what you found for $(-5x+2)(-5x+2)$ multiplied by $\frac{1}{9}$, i.e.
\[\frac{1}{9}\left(25x^2 - 20x + 4\right) = \frac{25}{9}x^2-\frac{20}{9}x+\frac{4}{9}\]
I hope this helps!
You can't combine $x$ and $x^2$ by addition or subtraction. The solution will have at least a term with $x^2$, a term with $x$ and a constant. If you already factored out the \(\displaystyle \frac{1}{9}\) then I think it's ok to call that the final answer but you can also distribute it to the other terms and get rid of the parentheses. That's the only thing left you can do to simplify the expression, so you are more or less doneIf I were to subtract 20x from 25x^2 this would leave 5x + 4, would this be the correct way?
I can't see that being the end of the problem?You can't combine $x$ and $x^2$ by addition or subtraction. The solution will have at least a term with $x^2$, a term with $x$ and a constant. If you already factored out the \(\displaystyle \frac{1}{9}\) then I think it's ok to call that the final answer but you can also distribute it to the other terms and get rid of the parentheses. That's the only thing left you can do to simplify the expression, so you are more or less done![]()
OK from this point onwards some people could now say that this is going to be in the wrong thread if I post as this is a circle problem, so I guess I should ask if I am permitted to continue or start another thread in geometry?What is the full problem you are trying to solve? I can't make sense of your post until I know that. My previous post was talking about using the FOIL method to remove the parentheses on \(\displaystyle \left(-\frac{5}{3}x+\frac{2}{3}\right)\left(-\frac{5}{3}x+\frac{2}{3}\right)\) and then simplifying the result as much as possible.
What is supposed to be equal to what?Please post the whole question and we'll get to the bottom of it.
The main point of my previous post was commenting that \(\displaystyle (25x^2-20x) \ne 5x\) for any $x$ and so you can't simplify the expression that way.
Thank you for being so aware of our forum rules! You make a good pointOK from this point onwards some people could now say that this is going to be in the wrong thread if I post as this is a circle problem, so I guess I should ask if I am permitted to continue or start another thread in geometry?