Question
Expand $(x+y)^{6}$.
✓
Answer
$(x+y)^{6}$
$={ }^{6} \mathrm{C}_{0}(x)^{6}(y)^{0}+{ }^{6} \mathrm{C}_{1}(x)^{5}(y)^{1}+{ }^{6} \mathrm{C}_{2}(x)^{4}(y)^{2}+{ }^{6} \mathrm{C}_{3}(x)^{3}(y)^{3}$ $+{ }^{6} \mathrm{C}_{4}(x)^{2}(y)^{4}+{ }^{6} \mathrm{C}_{5}(x)^{1}(y)^{5}+{ }^{6} \mathrm{C}_{6}(x)^{0}(y)^{6}$
$=x^{6}+6 x^{5} y+15 x^{4} y^{2}+20 x^{3} y^{3}+15 x^{2} y^{4}+6 x y^{5}+y^{6}$
$={ }^{6} \mathrm{C}_{0}(x)^{6}(y)^{0}+{ }^{6} \mathrm{C}_{1}(x)^{5}(y)^{1}+{ }^{6} \mathrm{C}_{2}(x)^{4}(y)^{2}+{ }^{6} \mathrm{C}_{3}(x)^{3}(y)^{3}$ $+{ }^{6} \mathrm{C}_{4}(x)^{2}(y)^{4}+{ }^{6} \mathrm{C}_{5}(x)^{1}(y)^{5}+{ }^{6} \mathrm{C}_{6}(x)^{0}(y)^{6}$
$=x^{6}+6 x^{5} y+15 x^{4} y^{2}+20 x^{3} y^{3}+15 x^{2} y^{4}+6 x y^{5}+y^{6}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the value of $f(0)$ for a real function $f(x)=16 x^2-16^x+x$.
→The data regarding area under cultivation of various crops at farms of two villages is given below. Present it through pictogram.
Find geometric mean of the numbers $1, 9, 81.$
→The common ratio of a G.P. is 3 and the sum of its first four terms is 400, write the G.P.
If three positive numbers k + 1, 3k — 1, 5k + 1 are in GR, find the value of k.
In an interview, $6$ questions are asked to a person. In how many ways can a person give $(I)$ at least $4$ correct answers $‘.’ (2)$ at the most $3$ correct answers ?
→Find the unknown value: ${ }^{n} C_{n-2}=15$
→Find variance of observations $11, 20, 29, 38, 52.$
→Frequency distribution of number of cars arrived on different days at a service station is as follows.
| No. of cars | 5 | 6 | 7 | 8 | 9 | 10 |
| No. of days | 5 | 10 | 15 | 8 | 7 | 5 |
The number of printing mistakes per page of a book of $60$ pages is as follows. Prepare a suitable frequency distribution using the data.
$2, 7, 5, 3, 1, 4, 5, 0, 2, 3, 9, 5, 6, 4, 2, 4, 5, 3, 2, 3, 8, 6, 5, 7, 9, 6, 7, 5, 9,$
$1, 4, 3, 0, 7, 5, 2, 1, 3, 4, 2, 5, 6, 2, 3, 6, 1, 3, 4, 6, 2, 2, 4, 5, 8, 5, 6, 8, 5, 9, 0.$
→$2, 7, 5, 3, 1, 4, 5, 0, 2, 3, 9, 5, 6, 4, 2, 4, 5, 3, 2, 3, 8, 6, 5, 7, 9, 6, 7, 5, 9,$
$1, 4, 3, 0, 7, 5, 2, 1, 3, 4, 2, 5, 6, 2, 3, 6, 1, 3, 4, 6, 2, 2, 4, 5, 8, 5, 6, 8, 5, 9, 0.$