Answer:
32[tex]x^{5}[/tex] - 80[tex]x^{4}[/tex] + 80x³ - 40x² + 10x - 1
Step-by-step explanation:
Using the 5 th row of Pascal's triangle to generate the coefficients
1 5 10 10 5 1
with deceasing powers of 2x from [tex](2x)^{5}[/tex] to [tex](2x)^{0}[/tex]
and increasing powers of - 1 from [tex](-1)^{0}[/tex] to [tex](-1)^{5}[/tex], then
[tex](2x-1)^{5}[/tex]
= 1 × [tex](2x)^{5}[/tex][tex](-1)^{0}[/tex] + 5 × [tex](2x)^{4}[/tex][tex](-1)^{1}[/tex] + 10 × (2x)³(- 1)² + 10 × (2x)²(- 1)³ + 5 × [tex](2x)^{1}[/tex][tex](-1)^{4}[/tex] + 1 × [tex](2x)^{0}[/tex][tex](-1)^{5}[/tex]
= 32[tex]x^{5}[/tex] - 80[tex]x^{4}[/tex] + 80x³ - 40x² + 10x - 1
