Using binomial evaluate the following: (98)^5 - Vidyadip

Question

Using binomial evaluate the following:
$(98)^5$

✓

Answer

We have,
$(98)^5=(100-2)^5$
$={^5\text{C}}_0\times100^5+{^5\text{C}}_1\times100^4\times(-2)+{^5\text{C}}_2\times100^3\times(-2)^2\\+{^5\text{C}}_3\times100^2\times(-2)^3+{^5\text{C}}_4\times100\times(-2)^4+{^5\text{C}}_5\times(-2)^5$
$={^5\text{C}}_0\times100^5-{^5\text{C}}_1\times100^4\times2+{^5\text{C}}_2\times100^3\times4\\-{^5\text{C}}_3\times100^2\times8+{^5\text{C}}_4\times100\times16-{^5\text{C}}_5\times32$
$=100^5-10\times100^4+40\times100^3-80\times100^2+80\times100-32$
$=10000000000-1000000000+40000000-800000+8000-32$
$=10040008000-1000800032$
$=9039207968$
$\therefore(98)^5=9039207968$

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