Question

Which expressions are equivalent to (j+j+2kj+j+2kj, plus, j, plus, 2, k)?

a) (2jk)
b) (2(j+j+k))
c) None of the above
d) (2jk + j + k)

Answer 1

The expression (j+j+2kj+j+2kj) simplifies to 2(j+j+k), making the correct answer b) (2(j+j+k)). It is the only choice that represents the original expression when it is factored correctly.

Step-by-step explanation:

The expression given is (j+j+2kj+j+2kj), which simplifies by combining like terms. The 'j' terms can be combined, and we get 2j since j+j equals 2j. Also, the 'kj' terms can be combined to get 2kj. When we put these together, we have (2j+2kj) which can be factored out as 2(j+kj), meaning that 2(j+j+k) is the simplified and equivalent expression.

Let's go through the options:

• (2jk) - This does not include the j term from the original expression, so it's not equivalent.
• (2(j+j+k)) - This is equivalent because it simplifies to 2(j(1+k)), which is the original expression factored correctly.
• None of the above - This is incorrect because option b is equivalent.
• (2jk + j + k) - This is not equivalent because it does not reflect the factored form of the original expression, and it does not group the terms correctly.

Therefore, the correct answer is b) (2(j+j+k)).