Answer:
See explanation
Step-by-step explanation:
Ana started the work nicely by multiplying out factors to get:\
[tex](x+4)(x+2)(2x+1)(x-2)=0[/tex]
She multiplied [tex](x+2)(x-2)[/tex] correctly using difference of two squares to get: [tex]x^2-4[/tex]
Unfortunately: She made a mistake in multiplying [tex](x+4)(2x+1)[/tex] she mistakenly got [tex]x^2+9x+4[/tex] instead of [tex]2x^2+9x+4[/tex]. She left out the coefficient of 2.
Therefore the second step should have been:
[tex](x^2-4)(2x^2+9x+4)[/tex]
The next step will now be:
[tex]2x^4+9x^3+4x^2-8x^4-36x-16=0[/tex]
This simplifies to
[tex]2x^4+9x^3-x^4-36x-16=0[/tex]