Pascal triangle

Question

(2x-3)³ expand using pascal triangle

Answer 1

(a+b)^3 = a^3 +3a^2b +3ab^2 + b^3

a's exponent decreases by each term,3,2,1,0 (a^0=1)

b's exponent increases by each term, 0,1,2,3 (b^0=1)

sum of exponents for each term = 3

coefficients are 3C3, 3C2, 3C1, 3C0

3C3 = 3!/3!0! =1

3C2 = 3!2!1! = 3

3C1 = 3!/1!2! =3

3C0 = 3!0!3! = 1

coefficients are 1,3,3,1, the 4th line of Pascal's triangle

1

11

121

1331

(2x-3)^3 = 8x^3 +3(2x)^2(-3) + 3(2x)(-3)^2 + (-3)^3

= 8x^3 -36x^2 +54x - 27

or multiply it out

(2x-3)^3 = (2x-3)(2x-3)(2x-3)

= (4x^2 -12x+9)(2x-3)

= 8x^3 -36x^2 +54x -27