Label the boxes to represent the expression.

Question

4(−4y+5)

Answer 1

To represent the expression \(4(-4y + 5)\) using labeled boxes, we can break it down step-by-step:

1. Start with the expression inside the parentheses, which is \(-4y + 5\). We will create two boxes to represent the terms inside:

   • Box 1: \(-4y\)
   • Box 2: \(5\)

2. Next, since we are multiplying the entire expression by \(4\), we will label a third box to represent the multiplication by \(4\):

   • Box 3: \(4\)

Now, we can label the boxes as follows:

• Box 1: \(-4y\)
• Box 2: \(5\)
• Box 3: represents the multiplication by \(4\)

Putting it all together, you can represent the expression \(4(-4y + 5)\) in terms of labeled boxes as:

• \[4 \times \text{(Box 1: -4y)} + 4 \times \text{(Box 2: 5)}\]

If you wish to simplify it, after multiplying each term by \(4\), you get:

• \(4 \times -4y = -16y\)
• \(4 \times 5 = 20\)

So, the full expression can also be represented after distribution as:

• \(-16y + 20\)

You could have separate boxes to show each term after distribution if needed:

• Box 1: \(-16y\)
• Box 2: \(20\)

This visual representation helps to understand both the original expression and the process involved in distribution.