i just want to ask....?

Question

this is finding the cube of a binomial.....
"^" means exponent

(2x+3)^3=8x^3+36x^2+54x+27

now my question is how could you get the 54????


thanks

Answer 1

Look at the factors; 54 = 2 * 3 * 3 * 3.
Now, when any binomial is cubed, the coefficients come from the 4th row of Pascal's triangle (1,3,3,1).

(a + b) ** 3 = a**3 + 3 * a**2 * b + 3 * a * b**2 + b**3

The term in x will have a coefficient of 3 (from Pascal's triangle) times 2 (because the x is already being multiplied by 2) times 9 (from the 3, which will be squared so the powers add up to 3) = 54.

Expand it fully and see for yourself.
(2x+3)(2x+3)(2x+3)
= (2x+3)(4x**2 + 12x + 9)
= (8x**3 + 24x**2 + 18x + 12x**2 + 36x + 27)
= 8x**3 + 36x**2 + 54x + 27

Answer 2

by expanding the whole equation and simplifying like this.
(2x+3)^3 = (2x+3)(2x+3)(2x+3)

Expanding the first two brackets gives
4x^2+12x+9
therefore (2x+3)^3 = (4x^2+12x+9)(2x+3)

expanding gives

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

Answer 3

too difficult to ANSWER