MySQL slow select query

Have this query that is awfully slow:

SELECT bdp.id 
FROM bd_products bdp JOIN bd_productwords bdpw
ON bdp.id = bdpw.productid JOIN bd_words bdw
ON bdpw.wordid = bdw.id
WHERE bdp.price > 0
AND bdw.word = 'nike' 
ORDER BY bdpw.productid DESC

It returns 18217 rows and takes around 1,4 seconds to run 🙁

Removing the ORDER BY doesn't change the execution time. It stays around 1,4 seconds.

But if I remove the bd_products part like below, execution time improves to just 0,005 seconds.

SELECT DISTINCT bdpw.productid
FROM bd_productwords bdpw JOIN bd_words bdw
ON bdpw.wordid = bdw.id
WHERE bdw.word = 'nike'

It's not the bdp.price part that's the problem. Removing it like below doesn't change the execution time. It stays around 1,4 seconds.

SELECT bdp.id 
FROM bd_products bdp JOIN bd_productwords bdpw
ON bdp.id = bdpw.productid JOIN bd_words bdw
ON bdpw.wordid = bdw.id
WHERE bdw.word = 'nike' 
ORDER BY bdpw.productid DESC
LIMIT 100

The table bd_products contain 2,0 million rows. bd_productwords contain 16,1 million rows and bd_words contain 0,4 million rows.

Any ideas for why execution time is so slow when I include the bd_products part?

Table columns:

bd_words: id (int), word (varchar)
bd_productwords: id (int), wordid (int), productid (int)
bd_products: id (int), name (varchar), description (varchar), price (int)

Indexes for bd_products:

Table   Non_unique  Key_name    Seq_in_index    Column_name Collation   Cardinality Sub_part    Packed  Null    Index_type  Comment Index_comment
bd_products 0   PRIMARY 1   id  A   1837288 \N  \N      BTREE       
bd_products 1   Price   1   price   A   55675   \N  \N  YES BTREE       
bd_products 1   Imageuploaded   1   imageuploaded   A   2   \N  \N  YES BTREE       
bd_products 1   BrandId 1   brand   A   9669    \N  \N  YES BTREE       
bd_products 1   BrandId 2   id  A   1837288 \N  \N      BTREE       
bd_products 1   Id  1   id  A   1837288 \N  \N      BTREE       

Indexes for bd_productwords:

Table   Non_unique  Key_name    Seq_in_index    Column_name Collation   Cardinality Sub_part    Packed  Null    Index_type  Comment Index_comment
bd_productwords 0   PRIMARY 1   id  A   15757529    \N  \N      BTREE       
bd_productwords 1   WordidProductid 1   wordid  A   1313127 \N  \N  YES BTREE       
bd_productwords 1   WordidProductid 2   productid   A   15757529    \N  \N  YES BTREE       
bd_productwords 1   ProductidWordid 1   productid   A   5252509 \N  \N  YES BTREE       
bd_productwords 1   ProductidWordid 2   wordid  A   15757529    \N  \N  YES BTREE       
bd_productwords 1   WordId  1   wordid  A   1125537 \N  \N  YES BTREE       
bd_productwords 1   ProductId   1   productid   A   5252509 \N  \N  YES BTREE

Indexes for bd_words:

Table   Non_unique  Key_name    Seq_in_index    Column_name Collation   Cardinality Sub_part    Packed  Null    Index_type  Comment Index_comment
bd_words    0   PRIMARY 1   id  A   395359  \N  \N      BTREE       
bd_words    1   Word    1   word    A   395359  \N  \N  YES BTREE       

Explain for the awfully slow query:

id  select_type table   type    possible_keys   key key_len ref rows    Extra
1   SIMPLE  bdw ref PRIMARY,Word    Word    603 const   1   Using where; Using index; Using temporary; Using filesort
1   SIMPLE  bdpw    ref WordidProductid,ProductidWordid,WordId,ProductId    WordidProductid 5   dreammodels local.bdw.id    12  Using where; Using index
1   SIMPLE  bdp eq_ref  PRIMARY,Price,Id    PRIMARY 4   dreammodels local.bdpw.productid    1   Using where