Answer:
The fourth term is [tex]-160x^{3}y^3[/tex].
Step-by-step explanation:
The given binomial expression is [tex](x-2y)^6[/tex].
When we compare this to the general binomial expression, [tex](a+b)^n[/tex], we have [tex]a=x,b=-2y,n=6[/tex].
The specific term in a binomial expansion with an integral index is given by:
[tex]T_{r+1}=\binom{n}{r}a^{n-r}b^r\:\:or\:\:T_{r+1}=^nC_ra^{n-r}b^r[/tex].
To find the fourth term, we set [tex]r+1=4[/tex]. This implies that;[tex]r=4-1=3[/tex].
We now substitute the values into the formula to obtain:
[tex]T_{3+1}=\binom{6}{3}x^{6-3}(-2y)^3[/tex].
We simplify to get:
[tex]T_{4}=20x^{3}(-8y^3)[/tex].
[tex]T_{4}=-160x^{3}y^3[/tex].
Therefore the fourth term is [tex]-160x^{3}y^3[/tex].
