Reviow \& Refrosh Video solutions at LarsanPrgealgulus, 60 m Using the Distributive Property In Dxerelses 81-84, use the Distributive Property to rewrite the expression, Simplify your results. 81. \( 3(7 x+1) \) 82. \( 5(x-6) \) 83. \( 6(x-1)+4 \) 84. \( 4(x+2)-12 \)

Sure! Let's solve each of the exercises (81-84) using the Distributive Property and simplify the expressions step by step. ### Distributive Property Reminder: The Distributive Property states that for any real numbers \( a \), \( b \), and \( c \): \[ a(b + c) = ab + ac \] \[ a(b - c) = ab - ac \] Now, let's apply this property to each problem. --- ### Problem 81: \( 3(7x + 1) \) **Step 1:** Apply the Distributive Property. \[ 3(7x) + 3(1) \] **Step 2:** Multiply. \[ 21x + 3 \] **Simplified Expression:** \[ 21x + 3 \] --- ### Problem 82: \( 5(x - 6) \) **Step 1:** Apply the Distributive Property. \[ 5(x) - 5(6) \] **Step 2:** Multiply. \[ 5x - 30 \] **Simplified Expression:** \[ 5x - 30 \] --- ### Problem 83: \( 6(x - 1) + 4 \) **Step 1:** Apply the Distributive Property to the first term. \[ 6(x) - 6(1) + 4 \] **Step 2:** Multiply. \[ 6x - 6 + 4 \] **Step 3:** Combine like terms (\(-6\) and \(+4\)). \[ 6x - 2 \] **Simplified Expression:** \[ 6x - 2 \] --- ### Problem 84: \( 4(x + 2) - 12 \) **Step 1:** Apply the Distributive Property. \[ 4(x) + 4(2) - 12 \] **Step 2:** Multiply. \[ 4x + 8 - 12 \] **Step 3:** Combine like terms (\(+8\) and \(-12\)). \[ 4x - 4 \] **Simplified Expression:** \[ 4x - 4 \] --- Feel free to reach out if you have any more questions or need further clarification on these problems!