Ask Me Help Desk - 16m^2 - 16/25, I come up with {4m - 4/5} I may have the wrong sign I forgot how to do

16m^2 - 16/25, I come up with {4m - 4/5} I may have the wrong sign I forgot how to do

My question is do I have the right sign I forgot how to do this? 16m^2 - 16/25= I come up with (4m - 4/5) ^2.

Not quite right. If you expand out your answer you'll see it doesn't equal 4m^2-16/25:

$ (4m-\frac 4 5 )^2 = (4m- \frac 4 5) \times (4m- \frac 4 5) = 4m \times (4m- \frac 4 5) - \frac 4 5 \times (4m- \frac 4 5) = 16m^2 - \frac {16} 5 m - \frac {16} 5 m + \frac {16} {25} = 16m^2 - \frac {32} 5 m + \frac {16} {25} $

This tells you that (4m^2-4/5)^2 is not the answer.

What you have is something known as "the difference of two squares," and it can be factored as follows:

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

So for your problem you have

$ 16m^2 - \frac {16}{25} = (4m + \frac 4 5 )(4m - \frac 4 5 ) $

Try expanding the right hand side to verify this is correct.

Thank you so much, this was driving me crazy the only one I couldn't figure out. I had also come up with 16(m^2 - 1/25) You have made this easy enough to understand and thank you for your help.