You provided two mathematical expressions. Let me help you expand them: **b) \( (2r - 0.25s)^2 \):** This is a binomial squared, so we can use the formula \( (a - b)^2 = a^2 - 2ab + b^2 \) to expand it: \[ (2r - 0.25s)^2 = (2r)^2 - 2(2r)(0.25s) + (0.25s)^2 \] Expanding: \[ (2r)^2 = 4r^2 \] \[ -2(2r)(0.25s) = -1rs \] \[ (0.25s)^2 = 0.0625s^2 \] So the expanded form is: \[ 4r^2 - rs + 0.0625s^2 \] --- **e) \( \left(3p - \frac{1}{3}q\right)\left(\frac{1}{3}q + 3p\right) \):** This is the product of two binomials, so we will expand it by using the distributive property: \[ = (3p)(\frac{1}{3}q) + (3p)(3p) - \left(\frac{1}{3}q\right)\left(\frac{1}{3}q\right) - \left(\frac{1}{3}q\right)(3p) \] Now expand each term: \[ (3p)(\frac{1}{3}q) = pq \] \[ (3p)(3p) = 9p^2 \] \[ -\left(\frac{1}{3}q\right)\left(\frac{1}{3}q\right) = -\frac{1}{9}q^2 \] \[ -\left(\frac{1}{3}q\right)(3p) = -pq \] Now combine like terms: \[ pq - pq + 9p^2 - \frac{1}{9}q^2 \] The \( pq \) terms cancel out, leaving: \[ 9p^2 - \frac{1}{9}q^2 \] --- So the expanded forms of the expressions are: **b) \( 4r^2 - rs + 0.0625s^2 \)** **e) \( 9p^2 - \frac{1}{9}q^2 \)**