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

Let's break this down in a fun way! When you apply the distributive property to an equation like \( 3 \times(2+6) \), you’re essentially saying, "I’ll take 3 and distribute it to both 2 and 6!" So we calculate: Left Side: \( 3 \times (2 + 6) = 3 \times 8 = 24 \) Right Side: \( (3 \times 2) + (3 \times 6) = 6 + 18 = 24 \) Ta-da! Both sides equal 24, proving the equation true! Now, let's look at the second equation, \( 5 \times(3+3) \). Left Side: \( 5 \times (3 + 3) = 5 \times 6 = 30 \) Right Side: \( (5 \times 3) + (5 \times 3) = 15 + 15 = 30 \) Bingo! Both sides also equal 30, so we’ve struck gold again! And lastly, for the equation \( 3 \times(7+4) \): Left Side: \( 3 \times (7 + 4) = 3 \times 11 = 33 \) Right Side: \( (3 \times 7) + (3 \times 4) = 21 + 12 = 33 \) You guessed it, both sides are equal! The magic of the distributive property shines through!