9. Show that the following equations are frue, by using the distributive property. a. $$ 3 imes(2+6)=(3 imes 2)+(3 imes 6) $$ b. $$ 5 imes(3+3)=(5 imes 3)+(5 imes 3) $$ c. $$ 3 imes(7+4)=(3 imes 7)+(3 imes 4) $$

Question

9. Show that the following equations are frue, by using the distributive property. a. $$ 3 	imes(2+6)=(3 	imes 2)+(3 	imes 6) $$ b. $$ 5 	imes(3+3)=(5 	imes 3)+(5 	imes 3) $$ c. $$ 3 	imes(7+4)=(3 	imes 7)+(3 	imes 4) $$

UpStudy AI · Accepted Answer

To show that each of the given equations is **true** using the **distributive property**, we'll apply the property step by step. The distributive property states that:

$$ a \times (b + c) = (a \times b) + (a \times c) $$

Let's verify each equation accordingly.

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### a. $$ 3 \times (2 + 6) = (3 \times 2) + (3 \times 6) $$

**Step 1: Apply the Distributive Property**

$$ 3 \times (2 + 6) = (3 \times 2) + (3 \times 6) $$

**Step 2: Perform the Multiplications**

$$ = 6 + 18 $$

**Step 3: Add the Results**

$$ = 24 $$

**Verification:**

Both sides equal **24**, confirming the equation is true.

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### b. $$ 5 \times (3 + 3) = (5 \times 3) + (5 \times 3) $$

**Step 1: Apply the Distributive Property**

$$ 5 \times (3 + 3) = (5 \times 3) + (5 \times 3) $$

**Step 2: Perform the Multiplications**

$$ = 15 + 15 $$

**Step 3: Add the Results**

$$ = 30 $$

**Verification:**

Both sides equal **30**, confirming the equation is true.

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### c. $$ 3 \times (7 + 4) = (3 \times 7) + (3 \times 4) $$

**Step 1: Apply the Distributive Property**

$$ 3 \times (7 + 4) = (3 \times 7) + (3 \times 4) $$

**Step 2: Perform the Multiplications**

$$ = 21 + 12 $$

**Step 3: Add the Results**

$$ = 33 $$

**Verification:**

Both sides equal **33**, confirming the equation is true.

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Each equation has been verified using the distributive property, demonstrating that the property holds true in these cases.
All three equations are true when the distributive property is applied.

Show that the following equations are frue, by using the
distributive property.
a.
b.
c.

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Show that the following equations are frue, by using the distributive property. a. b. c.

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Show that the following equations are frue, by using the
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