For eoch expression below, rewrite the subtraction as oddition of the opposite and combine the like terms. Verify that your simplified expression is equivalent to the ariginal expression a. \( 2 y-9 z^{2}-4 y \) b. \( 2 z-9 y z=3 y \cdot r y \)

To rewrite the subtraction as addition of the opposite and combine like terms for each expression, let's go through them one by one. ### a. \( 2y - 9z^2 - 4y \) 1. Rewrite the subtraction as addition of the opposite: \[ 2y + (-9z^2) + (-4y) \] 2. Combine like terms: \[ (2y - 4y) + (-9z^2) = -2y - 9z^2 \] So, the simplified expression is: \[ -2y - 9z^2 \] **Verification:** The original expression was \( 2y - 9z^2 - 4y \). If we substitute the simplified expression back: \[ 2y - 4y - 9z^2 = -2y - 9z^2 \] This confirms that the simplified expression is equivalent to the original expression. ### b. \( 2z - 9yz = 3y \cdot ry \) 1. First, let's rewrite the equation: \[ 2z - 9yz - 3y \cdot ry = 0 \] 2. Rewrite the subtraction as addition of the opposite: \[ 2z + (-9yz) + (-3y \cdot ry) = 0 \] 3. Combine like terms: \[ 2z - 9yz - 3y \cdot ry = 0 \] Since there are no like terms to combine further, we can leave it as: \[ 2z - 9yz - 3y \cdot ry = 0 \] **Verification:** The original expression was \( 2z - 9yz = 3y \cdot ry \). If we rearrange it: \[ 2z - 9yz - 3y \cdot ry = 0 \] This confirms that the simplified expression is equivalent to the original expression. ### Summary: - For part (a), the simplified expression is \( -2y - 9z^2 \). - For part (b), the expression remains \( 2z - 9yz - 3y \cdot ry = 0 \).