Select the expressions that are equivalent to 5(2u – 8)

Select the expressions that are equivalent to 5(2u – 8) .
(2u – 8) * 5
5(u + u – 8)
10u – 40
5(- 8 + 2u)

The correct answer and explanation is:

The expressions that are equivalent to 5(2u−8)5(2u – 8) are:

1. (2u−8)×5(2u – 8) \times 5
2. 10u−4010u – 40
3. 5(−8+2u)5(-8 + 2u)

Explanation:

To determine which expressions are equivalent, let’s break down the original expression 5(2u−8)5(2u – 8):

1. Distribute the 5 across the terms inside the parentheses: 5(2u−8)=5×2u−5×8=10u−405(2u – 8) = 5 \times 2u – 5 \times 8 = 10u – 40 This shows that the simplified form of 5(2u−8)5(2u – 8) is 10u−4010u – 40.
2. Check (2u−8)×5(2u – 8) \times 5:
   The expression (2u−8)×5(2u – 8) \times 5 is just a rearranged form of the original expression, where multiplication is commutative (i.e., a×b=b×aa \times b = b \times a). So this is equivalent to the original expression.
3. Check 5(u+u−8)5(u + u – 8):
   Simplifying this expression: 5(u+u−8)=5(2u−8)5(u + u – 8) = 5(2u – 8) This simplifies back to the original expression, so it is indeed equivalent.
4. Check 5(−8+2u)5(-8 + 2u):
   Since addition is commutative, −8+2u-8 + 2u is the same as 2u−82u – 8. So: 5(−8+2u)=5(2u−8)5(-8 + 2u) = 5(2u – 8) This expression is also equivalent to the original expression.

Thus, the correct equivalent expressions are:

• (2u−8)×5(2u – 8) \times 5
• 10u−4010u – 40
• 5(−8+2u)5(-8 + 2u)

Each of these expressions is simply a different form of representing the original 5(2u−8)5(2u – 8).