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

Question

BlackTom AI · Accepted Answer

We start by expanding the squared binomial and then combine like terms step by step.
Option analysis begins by expanding (5a+2)^2: (5a+2)^2 = 25a^2 + 20a + 4.
Next, we subtract 3a: (25a^2 + 20a + 4) - 3a = 25a^2 + 17a + 4.
Finally, we add 9: (25a^2 + 17a + 4) + 9 = 25a^2 + 17a + 13.
Now evaluate each answer choice against this result.

Option a: 5a^2 + 23a + 13 (as given in the first part of the option) does not match the expanded form since the coefficient of a^2 is incorrect (5a^2 instead of 25a^2) and the linear term 23a does not align with 17a. This shows a miscalculation in the squared term or the combination process.

Option b: 25a^2 + 17a + 13 (the expanded form we calculated) has the correct a^2 coefficient, the correct a-term, and the constant term matches after including the +9. This aligns with the step-by-step expansion and combining like terms.

Option c: 25a^2 − 3a + 13 changes the linear term to −3a, which would correspond to omitting the +20a from the expansion of (5a+2)^2 and incorrectly applying the subsequent subtraction and addition. This contradicts the actual combination, so it is not correct.

Option d: 5a^2 + 17a + 13 again has an incorrect a^2 coefficient (5a^2 instead of 25a^2). The discrepancy in the squared term means this cannot be the correct simplification.

In summary, the only option whose coefficients match the correctly expanded and simplified expression 25a^2 + 17a + 13 is the one containing that exact polynomial form. The comparison shows that the expanded square contributes 25a^2 and 20a, then the linear and constant terms are adjusted by −3a and +9 to arrive at the final constant and linear terms.

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

查看解析

登录即可查看完整答案

类似问题

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

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

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

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

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)

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

更多留学生实用工具

考试浏览器助手

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