memorize, mesmerize

Memorize or memorize means to learn by heart; to commit to memory--
He won't come out; he has to stay in and memorize his lines for the play.
He is trying to memorize his favorite poem.

Mesmerize or mesmerize means to hypnotize; to fascinate--
He uses the sound of a ticking clock to mesmerize his subjects.
If you stare at that design for a while, it may begin to mesmerize you.

Now that you know that, you can say--
"His friend, a psychology student, offered to mesmerize him, to help him memorize his science text."

memories, memorize

Memories or memories ( mem or eez ) is the plural ( more than one ) of "memory", meaning something kept in mind, or brought to mind from what someone has learned or experienced--
The old people like to sit and share memories of when they were young.
He had a lot of fond memories of his life back home on the farm.
Memories may also be the plural of "memory", meaning the mental faculty, or ability to remember--
Many old people have trouble with their memories.
Our memories get a real workout in this class.

Memorize or memorize ( mem or ize ) means to commit to memory, so as to be able to recall at some future time--for an exam or test, for example--
We have to memorize all of these vocabulary words for a quiz on Friday.
I am trying to memorize all of the important points in this chapter, but I keep forgetting some of them.

Now that you know that you can say--
"The students were sure that their memories were worn out, after all the words they had to memorize."

Note--"memory's" ( rhymes with memories ) may be the possessive ( belonging to ) form of "memory"--
The new medication should improve his memory's function.
"Memory's" may also be a contraction ( short, informal form ) of "memory is"--
His memory's not what it used to be.