ANSWER
[tex]T_{6}= - 84x^{2}[/tex]
EXPLANATION
The given binominal expression is
[tex] {(2x - 1)}^{7} [/tex]
When we compare to
[tex] {(a + b)}^{n} [/tex]
[tex]n=7,a=2x,b=-1 [/tex]
We want to find the sixth term.
This is given by the formula,
[tex]T_{r + 1}=nC_ra^{n-r}b^r[/tex]
where
[tex]r + 1 = 6[/tex]
[tex]r = 5[/tex]
The sixth term is given by
[tex]T_{6}=7C_5(2x)^{7-5}( - 1)^5[/tex]
.
[tex]T_{6}=7C_5(2x)^{2}( - 1)^5[/tex]
[tex]T_{6}= - 21 \times 4x^{2}[/tex]
[tex]T_{6}= - 84x^{2}[/tex]
