question_answer 16)

Verify the following: (a) \[\text{18}\times [\text{7}+(-\text{ 3})]=[\text{18}\times \text{7}]+[\text{18}\times (-\text{ 3})]\] (b) \[\text{(}-\text{21)}\times [(-\text{ 4})+(-\text{ 6})]\]\[=[(-\text{21})\times (-\text{ 4})]+[(-\text{21})\times (-\text{ 6})].\]                

Answer:

                (a) \[18\times [7+(-3)]=[18\times 7]+[18\times (-3)]\] L.H.S. \[=\text{18}\times [\text{7}+(-\text{ 3})]=\text{18}\times [(\text{7}-\text{3})]\]\[=\text{18}\times (\text{4})=\text{18}\times \text{4}=\text{72}\] R.H.S. \[=[\text{18}\times \text{7}]+[\text{18}\times (-\text{ 3})]=\text{126}+[-\text{ (18}\times \text{3)}]\]\[=\text{126}+(-\text{ 54})=\text{126}-\text{54}=\text{72}\] So, \[\text{18}\times [\text{7}+(-\text{ 3})]=[\text{18}\times \text{7}]+[\text{18}\times (-\text{3})]\] (b) \[(-21)\times [(-4)+(-6)]\]\[\mathbf{ }=[(-\mathbf{ }21)\times (-4)]+[(-21)\times (-6)]\] L.H.S. \[=(-\text{ 21})\times (-\text{ 1}0)\]\[=\text{21}\times \text{1}0=\text{21}0\] R.H.S. \[=[(-\text{ 21})\times (-\text{ 4})]+[(-\text{ 21})\times (-\text{ 6})]\]\[=(\text{21}\times \text{4})+(\text{21}\times \text{6})=\text{84}+\text{126}=\text{21}0\] So, \[\text{(}-\text{21)}\times [(-\text{ 4})+(-\text{ 6})]\]\[=[(-\text{ 21})\times (-\text{ 4})]+\]\[[(-\text{ 21})\times (-\text{ 6})]\]