Expand and simplify the following:[math: (2x−3)3] (2x-3)^3

Question

BlackTom AI · Accepted Answer

Let's parse the task carefully: expand and simplify (2x − 3)^3, and compare to the given options.
Option a: 8x^3 + 36x^2 − 54x + 27. This has the correct 8x^3 leading term, but the signs of the middle terms are all wrong compared to the actual expansion, which should alternate signs starting with a negative x^2 term. Specifically, the x^2 term should be negative, not positive, and the constant term should be negative, not positive.
Option b: 8x^3 − 27. This only includes the cube terms from the expansion of a binomial and omits the x^2 and x terms entirely. Since (2x − 3)^3 generates three additional terms beyond 8x^3, this option is incomplete and therefore incorrect.
Option c: 8x^3 − 12x^2 + 18x − 27. Here the x^2 term is −12x^2 instead of the correct −36x^2, and the x term is +18x instead of +54x. The coefficients are not consistent with the binomial expansion formula (a − b)^3 = a^3 − 3a^2b + 3ab^2 − b^3 when a = 2x and b = 3, so this option misapplies the coefficients.
Option d: 8x^3 − 36x^2 + 54x − 27. This matches the binomial expansion exactly: a^3 = (2x)^3 = 8x^3, −3a^2b = −3(2x)^2(3) = −3(4x^2)(3) = −36x^2, +3ab^2 = 3(2x)(3^2) = 3(2x)(9) = 54x, and −b^3 = −3^3 = −27. All terms have the correct coefficients and signs.
In summary, options a, b, and c each contain specific inaccuracies—the wrong signs or missing terms or incorrect coefficients—whereas option d faithfully reflects the correct binomial expansion of (2x − 3)^3.

Expand and simplify the following:[math: (2x−3)3] (2x-3)^3单项选择题

类似问题

Select the expression that is equal to: (3k+1)2.

Select the correct answer for: Simplify ( 𝑥 − 3 ) 2

Multiply and simplify. ( 3 𝑥 − 2 𝑦 ) 2

Expand and simplify the following expression:[math: (5a+2)2−3a+9] (5a+2)^2-3a+9

Determine the 2nd term in the binomial expansion of (a + 3b$$)^4 .(C:1)

Question text Determine the constant term of the expansion for the expression (2x^3 -4)^5 using the general term. Fill in the blanks below do not use any spaces:Fill in the blank r = Answer 1 Question 44[input]Constant term = Answer 2 Question 44[input](C:2)

Given the expression (2x+3y^2)^5 , determine the total number of terms in its expansion:(K:1)

Which of the following trees corresponds to a potential parse of the ambiguous sentence below, with correct syntactic categories? Some diagnostics are provided.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单