Question
Using binomial theorem, write down the expansions of the following:
(2x - 3y)4
Using binomial theorem, write down the expansions of the following:
(2x - 3y)4
The expansion of (x + y)n has n + 1 term so, the expansion of (2x - 3y)4 has 5 terms.
Using binomial theorem, we have
$(2\text{x}-3\text{y})^4={^4\text{C}_0}(2\text{x})^4(3\text{y})^0-{^4\text{C}}_1(2\text{x})^3(3\text{y})^1\\+{^4\text{C}}_2(2\text{x})^2(3\text{y})^2-{^4\text{C}}_3(2\text{x})^1(3\text{y})^3+{^4\text{C}}_4(2\text{x})^0(3\text{y})^4$
$=2^4\text{x}^4-4\times2^3\times3\text{x}^3\text{y}+6\times2^2\times3^2\times\text{x}^2\text{y}^2\\-4\times2\times3^3\times\text{xy}^3+\text{3}^4\text{y}^4$
$=16\text{x}^4-96\text{x}^3\text{y}+216\text{x}^2\text{y}^2-216\text{xy}^3+81\text{y}^4$
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