Answer:
B) 720.
Step-by-step explanation:
We can use the Binomial Expansion Theorem:
[tex]\displaystyle (a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^kb^{n-k}[/tex]
We have the expression:
[tex]\displaystyle (2x-3)^5[/tex]
Therefore, a = 2x, b = -3, and n = 5.
We want to find the coefficient of x³. To get x³, we can cube a. Therefore, we can find our coefficient by letting k = 3. Hence:
[tex]\displaystyle \binom{5}{3}(2x)^3(-3)^{5-3}[/tex]
Evaluate:
[tex]\displaystyle =10(8x^3)(9)=720x^3[/tex]
Our answer is B.
