Question

Factor (x^2-2x)+1-9z^2

Answer 1

does it help to know that
\[x^2-2x+1=(x-1)^2\]?

Answer 2

that gives you
\[(x-1)^2-9z^2\] which is the difference of two squares, and you can factor as
\[a^2-b^2=(a+b)(a-b)\]with
\[a=(x-1)\] and \[b=3z\]

Answer 3

this is the answer (x-1+3z)(x-1-3z) I need to know the steps of how to get this answer

Answer 4

did you understand the last one i wrote?
\[a^2-b^2=(a+b)(a-b)\] so
\[(x-1)^2-9z^2=(x-1+3z)(x-1-3z)\]

Answer 5

the gimmick is to recognize that
\[x^2-2x+1=(x-1)^2\]

Answer 6

\[\large \color{blue}a^2-\color{red}b^2=(\color{red}a+\color{blue}b)(\color{red}a-\color{blue}b)\]\[\large \color{red}{(x-1)}^2-\color{blue}{3z}^2\]
\[\huge =(\color{red}{x-1}+\color{blue}{3z})(\color{red}{x-1}-\color{blue}{3z})\]

Answer 7

how do factor a^3+125 using the difference of two cubes

Answer 8

it is not the difference of two cubes, it is the sum of two cubes