Question

Expand the binomial (1-3x)⁵ upto the term having x³​

Answer 1

Step-by-step explanation:

We know that,

$\sf {(1 + x)}^{n} \\ =\sf {1}^{n} +^nC_ 1 {x}^{1} + ^nC_2 {x}^{2} + ... + ^nC_r {x}^{r} + ... + {x}^{n}$

Now,

$\bf {(1 - 3x})^{5} \\ \\ \bf = {1}^{5} + ^5C_1 .{( - 3x)}^{1} + ^5C_2. {( - 3x)}^{2} + ^5C_3. {( - 3x)}^{3} + ... \\ \\ \bf = 1 - 5 \times 3x + 10 \times 9 \times {x}^{2} - 10 \times 27 {x}^{3} + ... \\ \\ \bf = 1 - 15x + 90 {x}^{2} - 270 {x}^{3} + ...$