Identify which of the commutative, associative, and/or distributive laws are being illustrated in the following examples: \( \begin{array}{ll}\text { Q.2.3.1 } & \text { Distributive law }(15 \times 7) \times 9=15 \times 7 \times 9 \\ \text { Q.2.3.2 } & 29 \times(5+17)=29 \times 5+29 \times 17\end{array} \)

We start with the two expressions and determine which algebraic law each one illustrates. ### Q.2.3.1 The expression is \[ (15 \times 7) \times 9 = 15 \times 7 \times 9. \] Here, the grouping of the factors is changed without altering the order. In general, the associative law for multiplication states that \[ (a \times b) \times c = a \times (b \times c). \] In this expression, the parentheses are removed, which is a direct application of the associative law. Therefore, **Q.2.3.1 illustrates the associative law**. ### Q.2.3.2 The expression is \[ 29 \times (5+17)=29 \times 5+29 \times 17. \] In this case, the multiplication is distributed over the addition inside the parentheses. The distributive law states that \[ a \times (b+c)=a \times b+a \times c. \] Thus, **Q.2.3.2 illustrates the distributive law**. In summary: - Q.2.3.1 uses the **associative law**. - Q.2.3.2 uses the **distributive law**.