Questions: Can you think of another way to show that all three expressions are equivalent? How can you use properties of operations to decide whether or not expressions are equivalent? Use what you just learned about equivalent expressions to solve these problems. Show your work on a separate sheet of paper. The perimeter of a square is given as 12x+20. Write two different expressions to represent its perimeter. Use factoring for one way. Write two different expressions equivalent to 8d-4.

Can you think of another way to show that all three expressions are equivalent?

How can you use properties of operations to decide whether or not expressions are equivalent?

Use what you just learned about equivalent expressions to solve these problems. Show your work on a separate sheet of paper.
The perimeter of a square is given as 12x+20. Write two different expressions to represent its perimeter. Use factoring for one way.

Write two different expressions equivalent to 8d-4.

Transcript text: 5 Can you think of another way to show that all three expressions are equivalent? $\qquad$ $\qquad$ 6. How can you use properties of operations to decide whether or not expressions are equivalent? $\qquad$ $\qquad$ $\qquad$ Try It Use what you just learned about equivalent expressions to solve these problems. Show your work on a separate sheet of paper. $(7)$ The perimeter of a square is given as $12 x+20$. Write two different expressions to represent its perimeter. Use factoring for one way. $\qquad$ L_ White two different expressions equivalent to $8 d-4$.

Solution

Solution Steps

Step 1: Show that all three expressions are equivalent

To demonstrate that all three expressions are equivalent, you can simplify each expression to the same form or show that they can be transformed into one another using algebraic properties such as the distributive property, commutative property, or factoring.

Step 2: Use properties of operations to decide whether expressions are equivalent

To determine if expressions are equivalent, apply properties of operations such as:

Distributive Property: Expand or factor expressions to see if they match.
Commutative Property: Rearrange terms to check for equivalence.
Combining Like Terms: Simplify expressions by combining similar terms.

Step 3: Write two different expressions for the perimeter of a square

Given the perimeter of a square as $12x + 20$, two equivalent expressions can be:

Factored Form: Factor out the greatest common factor (GCF) of 4: \[ 12x + 20 = 4(3x + 5) \]
Expanded Form: Distribute the GCF back to verify equivalence: \[ 4(3x + 5) = 12x + 20 \]

Step 4: Write two different expressions equivalent to $8d - 4$

Two equivalent expressions for $8d - 4$ are:

Factored Form: Factor out the GCF of 4: \[ 8d - 4 = 4(2d - 1) \]
Alternative Form: Rewrite the expression by splitting the terms: \[ 8d - 4 = 8d - 4 + 0 \]