Question

do these two expressions represent equivalent expressions? explain why or why not.

(36 + 20) \t (4(9 + 5))

Explanation:

Find the greatest common factor

Using the Greatest Common Factor knowledge point

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Apply the distributive property

Using the Distributive Property knowledge point

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Compare the two expressions

We compare the original sum to the factored expression.

• The first expression is \(36 + 20\).
• The second expression is \(4(9 + 5)\).
• Factoring out the GCF of 4 shows they are identical.
• Both expressions simplify to the same value:

$$ 36 + 20 = 56 $$

$$ 4(9 + 5) = 4(14) = 56 $$

Answer:

Yes, these two expressions represent equivalent expressions.

By finding the greatest common factor (GCF) of 36 and 20, which is 4, we can rewrite the expression \(36 + 20\) using the distributive property:

$$36 + 20 = 4(9) + 4(5) = 4(9 + 5)$$

Since both expressions can be written in the same form and both simplify to 56, they are equivalent.