Question

Step-by-step solution in how to factor x^4-7x^2y^2+9y^2

Answer 1

Question: Can you factor a^2 - 7a + 9 ? If so, then the posted expression will factor? If not, then the posted expression will not factor. @elleblythe

Answer 2

\[\huge x^4-7x^2y^2+9y^2\]
\[\large there~ are~ two~factors \]
\[\large one~factor:-\]
\[\huge x^2(x^2-7y^2)+9y^2\]
\[\large second~factor:-\]
\[\huge x^4+y^2(9-7x^2) ~~~~OR~~~ x^4+(9-7x^2)y^2\]

Answer 3

Those are not factors.

Answer 4

@Directrix @mayankdevnani the answer is supposed to be (x^2-xy-3y^2)(x^2+xy-3y^2) but what's the solution?

Answer 5

@Directrix thank you.... now i can factor this.. please wait

Answer 6

ok, then the question has a typo

Answer 7

check if the given expression is :-
\(x^4-7x^2y^2+9\color{red}{y^4}\)

Answer 8

sorry my bad! the given expression is x^4−7x^2y^2+9y^4. thanks for correcting me @ganeshie8

Answer 9

\(x^4-7x^2y^2+9y^4\)

say,
\(x^2=m, y^2=n\)

\(m^2-7mn+9n^2\)

\((m-3n)^2 -mn\)

\((x^2-3y^2)^2 - x^2y^2\)

\((x^2-3y^2+xy)(x^2-3y^2-xy)\)

Answer 10

see if that makes some sense

Answer 11

\[\huge x^4 - 7x^2y^2 + 9y^4\]

\[\large we~can~write~It~also~as:-\]
\[\huge x^4-6x^2y^2-x^2y^2+9y^4\]
\[\huge ~~~~~~~~~~~OR~~~~~~~~\]
\[\huge x^4-6x^2y^2+9y^4-x^2y^2\]
\[\huge (x^2-3y^2)^2-(xy)^2\]
\[\huge (x^2-3y^2+xy)(x^2-3y^2-xy)\]

Answer 12

understood or not? @elleblythe

Answer 13

got it thank you @ganeshie8 @mayankdevnani

Answer 14

welcome :)

Answer 15

np :) your questions are very tough :S

Answer 16

\begin{align}
\large \color{blue}{x^4}-7\color{green}{x^2y^2}+\color{blue}{9y^4} &= \large x^4 -6x^2y^2-x^2y^2 +9y^4 \\
&=\large \color{blue}{ x^4 -6x^2y^2+9y^4}-\color{green}{x^2y^2} \\
&= \large (x^2-3y^2)^2 -(xy)^2 \\
&=\large \color{blue}{(x^2 -3y^2)}^2 -\color{green}{(x^2y^2)} \\
&=\large (x^2-3y^2 +x^2y^2)(x^2-3y^2 -x^2y^2) \\
\end{align}

Answer 17

wow its nice ! where did u learn align tag @Jhannybean

Answer 18

By creeping on people's TeX formatting LOL

Answer 19

thats fast way to learn latex :) how do we control wat it aligns wid ?

Answer 20

&=

Answer 21

\(
\begin{align}
ganeshie &= g \\
&= a \\
&= n \\
&= e\\
&= s\\
&= h\\

\end{align}
\)

Answer 22

oh i forgot the \\ ahah.

Answer 23

\(
\begin{align}
Jhanny &bean \\
& J \\
& h \\
& a\\
& n\\
& n\\
& y\\

\end{align}
\)

Answer 24

aligned it to b

Answer 25

basically we can align it to watever we want, just put & before watever u want to align the next line to, nice :) feels like an expert lol