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What is the coefficient of x3 in the expansion of (2x−3)5?

Group of answer choices

a) -360

b) 720

c) 10

d) -5

e) -120

Sagot :

Wilhelm2idn

Answer:

B 720

Step-by-step explanation:

same process as the previous image I sent ya

XKelvinidn

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.

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