7 Find the value of each expression when \( a=5 \) and \( b=-11 \). a) \( 5+2 a^{2} \) b) \( (4 a)^{2} b \) c) \( 2(b+2 a)^{3} \)

Let's evaluate each expression step by step: **a)** For \( 5 + 2a^{2} \): Given \( a = 5 \), \[ a^2 = 5^2 = 25 \] Now substitute into the expression: \[ 5 + 2 \cdot 25 = 5 + 50 = 55 \] So, \( 5 + 2a^{2} = 55 \). --- **b)** For \( (4a)^{2}b \): Given \( a = 5 \) and \( b = -11 \), \[ 4a = 4 \cdot 5 = 20 \] Now calculate \( (20)^{2}b \): \[ (20)^{2} = 400 \] And then substitute \( b \): \[ 400 \cdot (-11) = -4400 \] So, \( (4a)^{2}b = -4400 \). --- **c)** For \( 2(b + 2a)^{3} \): Given \( b = -11 \) and \( a = 5 \), First, calculate \( b + 2a \): \[ b + 2a = -11 + 2 \cdot 5 = -11 + 10 = -1 \] Now raise it to the power of 3: \[ (-1)^{3} = -1 \] Now multiply by 2: \[ 2 \cdot (-1) = -2 \] So, \( 2(b + 2a)^{3} = -2 \). --- Final results: a) \( 55 \) b) \( -4400 \) c) \( -2 \)