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

To show that these equations are true using the distributive property, we'll break down each equation step-by-step. For the first equation: Left side: \( 3 \times (2 + 6) = 3 \times 8 = 24 \) Right side: \( (3 \times 2) + (3 \times 6) = 6 + 18 = 24 \) Both sides equal 24, so the equation holds true! For the second equation: Left side: \( 5 \times (3 + 3) = 5 \times 6 = 30 \) Right side: \( (5 \times 3) + (5 \times 3) = 15 + 15 = 30 \) Again, both sides equal 30, proving this equation is true! For the third equation: Left side: \( 3 \times (7 + 4) = 3 \times 11 = 33 \) Right side: \( (3 \times 7) + (3 \times 4) = 21 + 12 = 33 \) Both sides equal 33, confirming the equation is valid! Now you’ve successfully shown all three equations are true using the distributive property! It's a great way to foster your understanding of how multiplication interacts with addition. Keep practicing, and you'll become a pro in no time!