Question

Apply the Binomial Theorem to expand the following expression

Answer 1

Answer:

32$x^{5}$ - 80$x^{4}$ + 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 $(2x)^{5}$ to $(2x)^{0}$

and increasing powers of - 1 from $(-1)^{0}$ to $(-1)^{5}$, then

$(2x-1)^{5}$

= 1 × $(2x)^{5}$$(-1)^{0}$ + 5 × $(2x)^{4}$$(-1)^{1}$ + 10 × (2x)³(- 1)² + 10 × (2x)²(- 1)³ + 5 × $(2x)^{1}$$(-1)^{4}$ + 1 × $(2x)^{0}$$(-1)^{5}$

= 32$x^{5}$ - 80$x^{4}$ + 80x³ - 40x² + 10x - 1

Answer 2

Answer:

32x^5-80x^4+80x^3+32x^2+10x-1