Question

How do I factor 2m^2+4mn+2n^2-50b^2?

Answer 1

you can factor a 2 that is all

Answer 2

so what do you get after you factored a 2?

Answer 3

m^2+2mn+n^2-25b^2

Answer 4

yeh

Answer 5

hmm

Answer 6

But the answer should be 2(m+n+5b)(m+n-5b)
How do i get to this?

Answer 7

hold the mayo and onions

Answer 8

ooh so wanna factor by grouping?

Answer 9

Yes

Answer 10

Sorry should have clarified that

Answer 11

i dont see a way to factor by grouping here

Answer 12

\(\bf 2m^2+4mn+2n^2-50b^2\implies 2(m^2+2mn+n^2-25b^2)
\\ \quad \\
2[(m^2+2mn+n^2)-25b^2]\qquad recall\quad \begin{array}{cccccllllll}
{\color{brown}{ a}}^2& + &2{\color{brown}{ a}}{\color{blue}{ b}}&+&{\color{blue}{ b}}^2\\
\downarrow && &&\downarrow \\
{\color{brown}{ a}}&& &&{\color{blue}{ b}}\\
&\to &({\color{brown}{ a}} + {\color{blue}{ b}})^2&\leftarrow
\end{array}
\\ \quad \\
2[({\color{brown}{ m}}^2+2mn+{\color{blue}{ n}}^2)-25b^2]\implies 2[(m+n)^2-25b^2]
\\ \quad \\
2[(m+n)^2-({\color{purple}{ 5b }})^2]\)

expand that by "difference of squares"