Question #bad20

Answer 1:
#x(xy + 7)^3#

The question asks for a product of #x# and a factor that depends on #x#. Therefore you know that:

• You need to have multiplication of #x# and some other factor.
• Your other factor should change as you change #x#.

Hence, #x(xy + 7)^3# is your best bet, as you have multiplication, and your other factor - #(xy + 7)^3# - changes with #x#.

Answer 2:
#xz^5#

Again, you are asked for a product, but this time your factor does not depend on #x#. Therefore, you know:

• You must have multiplication of #x# and some other factor.
• Your other factor should not change as you change #x#.

So, #xz^5# is your best answer. You have multiplication, but #z# does not change with #x#.

Answer 3:
#yx + x# or #x + x(y+4)# or #x + 2xy^3#

Here, you're asked for a sum of two terms: #x#, and some multiple of #x#. So, you know that:

• You have addition of #x# and some other term.
• Your other term must be #x# multiplied by some factor (in terms of any other variable).

You have three answers that fulfill this criteria (listed above): all of them have #x# added to #x# times some factor (in terms of #y#).

Answer 4:
#x + (y+2)z#

Here, you're again asked for a sum, but this time your other term must not depend on #x#. Therefore, you know:

• You have addition of #x# and some other term.
• Your other term must not have #x# in it.

#x + (y+2)z# is your best choice here. Note that you have only #y# and #z# as variables in your 2nd term, and neither of those depend on #x#, making this your best answer.

Hope that helps :)