2а+ас²-а²с-2с, а=1⅓, с=1⅓

To evaluate the expression \( 2a + ac^2 - a^2c - 2c \) for \( a = \frac{4}{3} \) and \( c = \frac{4}{3} \), we follow these steps: 1. Substitute the values of \( a \) and \( c \) into the expression. \[ a = \frac{4}{3}, \quad c = \frac{4}{3} \] 2. Calculate each term: - Calculate \( 2a \): \[ 2a = 2 \times \frac{4}{3} = \frac{8}{3} \] - Calculate \( ac^2 \): \[ c^2 = \left(\frac{4}{3}\right)^2 = \frac{16}{9} \] \[ ac^2 = \frac{4}{3} \times \frac{16}{9} = \frac{64}{27} \] - Calculate \( a^2c \): \[ a^2 = \left(\frac{4}{3}\right)^2 = \frac{16}{9} \] \[ a^2c = \frac{16}{9} \times \frac{4}{3} = \frac{64}{27} \] - Calculate \( -2c \): \[ -2c = -2 \times \frac{4}{3} = -\frac{8}{3} \] 3. Now substitute these values into the whole expression: \[ 2a + ac^2 - a^2c - 2c = \frac{8}{3} + \frac{64}{27} - \frac{64}{27} - \frac{8}{3} \] 4. Notice that \( \frac{64}{27} - \frac{64}{27} = 0 \) and \( \frac{8}{3} - \frac{8}{3} = 0 \). Thus, the expression simplifies to: \[ 0 + 0 = 0 \] So the final result is: \[ \boxed{0} \]