Question

② 2(4 + 1.3x + 3y) ④ 0.5(3 + 1.3x + 5y) ⑦ 2.1x + 3y + 4.2x + 2.5y ⑨ 5x + 7.2y - 2.5x + 1.2y

Explanation:

Step1: Expand using distributive property

For ⑤:

$$\begin{align*} 0.2(4 + 1.2x + 3y) &= 0.2\times4 + 0.2\times1.2x + 0.2\times3y\\ &= 0.8 + 0.24x + 0.6y \end{align*}$$

For ⑥:

$$\begin{align*} 0.5(3 + 1.3x + 5y) &= 0.5\times3 + 0.5\times1.3x + 0.5\times5y\\ &= 1.5 + 0.65x + 2.5y \end{align*}$$

Step2: Combine like terms

For ⑦:

$$\begin{align*} 2.1x + 3y + 4.2x + 2.5y &= (2.1x + 4.2x) + (3y + 2.5y)\\ &= 6.3x + 5.5y \end{align*}$$

For ⑧:

$$\begin{align*} 5x + 7.2y - 2.5x + 1.2y &= (5x - 2.5x) + (7.2y + 1.2y)\\ &= 2.5x + 8.4y \end{align*}$$

Answer:

⑤ $0.8 + 0.24x + 0.6y$
⑥ $1.5 + 0.65x + 2.5y$
⑦ $6.3x + 5.5y$
⑧ $2.5x + 8.4y$