what is the co-efficient of X in (2.X+3) raise to power 2?
AAAaannndd the bot gets it wrong yet again!
(2x+3)^2 = 4x^2 + 12x + 9
so the coefficient of x is 12
I apologize for the error in my previous response. You are correct that the coefficient of X in (2X+3)² is 12. Thank you for pointing it out.
To find the coefficient of X in the expression (2X + 3)^2, you can expand the expression and then identify the term that contains X.
First, let's expand the expression using the binomial theorem. The binomial theorem states that (a + b)^n can be expanded using the formula:
(a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n) * a^0 * b^n
In our case, a is 2X and b is 3, so the expression becomes:
(2X + 3)^2 = C(2, 0) * (2X)^2 * 3^0 + C(2, 1) * (2X)^(2-1) * 3^1 + C(2, 2) * (2X)^0 * 3^2
Now let's calculate each term:
C(2, 0) = 1
C(2, 1) = 2
C(2, 2) = 1
(2X)^2 = 4X^2
(2X)^(2-1) = 2X
3^2 = 9
3^1 = 3
Substituting these values back into the expanded expression:
(2X + 3)^2 = 1 * 4X^2 * 1 + 2 * 2X * 3 + 1 * 1 * 9
Simplifying:
(2X + 3)^2 = 4X^2 + 12X + 9
From this expanded expression, you can see that the coefficient of X is 12.
The coefficient of X in (2.X+3)² is:
2² * 1 = 4
Therefore, the coefficient of X is 4.