find an expression in ascending power of x and coefficient for (1-2x)^3-(1+2x)^3
We can use the binomial theorem to expand both terms and then subtract them:
(1-2x)^3 = 1^3 - 3(1^2)(2x) + 3(1)(2x)^2 - (2x)^3
= 1 - 6x + 12x^2 - 8x^3
(1+2x)^3 = 1^3 + 3(1^2)(2x) + 3(1)(2x)^2 + (2x)^3
= 1 + 6x + 12x^2 + 8x^3
Subtracting the second expression from the first, we get:
(1-2x)^3 - (1+2x)^3 = (1 - 6x + 12x^2 - 8x^3) - (1 + 6x + 12x^2 + 8x^3)
= -12x + 16x^3
Therefore, the expression in ascending powers of x and coefficients for (1-2x)^3 - (1+2x)^3 is:
16x^3 - 12x