21. structure in expressions.docx

Structure in expressions 1. 4​2​​(20k)−7 Which of the following is equivalent to the above expression? A. 4​2​ ​(20+k)−7 B. 42 (20k) -7 C. 20k⋅4​2​​−7 D. (42·20k) -7 Correct Answer: C Difficult Level: 2 2. (5j​2​​k)​3​​+(θ−3) Which of the following is equivalent to the above expression? A. (θ−3)+(125k​3​​j​6​​) B. (θ−3)+(5j​2​​k​3​​) C. (125k​3​​j​6​​)+(3−θ) D. (5j​2​​k​3​​)+(3−θ) Correct Answer: A Difficult Level: 2 3. (4s​2​​t)​3​​+(p−3) Which of the following is equivalent to the above expression? A. (4​3​​s​23​​t​3​​)+(p−3) B. (p−3)+(4s​2​​t​3​​) C. (12s​2​​t)+(p−3) D. (p−3)+(64s​6​​t​3​​) Correct Answer: D Difficult Level: 2 4. x2-16（x-3）（x+6）÷(x+a)(a-x)x2+cx-18=-1 Given the equation above, what is the value of c? Correct Answer: 3 Difficult Level: 2 5. A​3​​+B​3​​=(C+8y)(D−40xy+E) A partial factorization of a sum of cubes is given above. Which of the following is equivalent to A+B? A. 13xy B. 20x+2y C. 2.5x+8y D. 5x+8y Correct Answer: D Difficult Level: 2 6. (x-y6)(x-y12) Which of the following is equivalent to the above expression for x≠y? A. 2 B.12 C. x-y2 D. (x-y)272 Correct Answer: A Difficult Level: 2 7. (n​6​​k​14​​)​5​​ Which of the following is equivalent to the above expression? A. (n​2​​k​5​​)​3​​ B. (n​3​​)​10​​(k​2​​)​7 C. (n​15​​k​35​​)​2​​ D. (n​5​​)​5​​(k​10​​)​7​​ Correct Answer: C Difficult Level: 2 8. abc+def Which of the following is equivalent to the above expression? A.abc+dfe B. abc+def C. bca+dfe D. bca+def Correct Answer: A Difficult Level: 2 9. The expression (x​2​​+h​2​​)(x​2​​−h​2​​) can be written as (1+m−p)x​4​​−mp where h, m, p, and b are constants. What is one possible value of m? A. 1 B. h C. h2 D. h4 Correct Answer: C Difficult Level: 2 10. (a+b+c)(a−b−c) Which of the following is equivalent to the above expression? A. a(b+c)−(a+b)c B. a​2​​(b+c)−(a+b)c​2​​ C. a​2​​−(b+c)​2​​ D. (a+b)​2​​−c​2 ​​ Correct Answer: C Difficult Level: 3 11. (3a+b)3(a+b) Which of the following is equivalent to the above expression for a≠−b? A. 1 B. 9 C. 1a2+b2 D. 1a2+2ab+b2 ​​ Correct Answer: D Difficult Level: 3 12. abxyijmn Which of the following is equivalent to the above expression? A. (ax)(im)(by)(jn) B. a(bm)nx(yi)j C. (ab)(ij)(xy)(mn) D. a(bx)yi(jm)n ​​ Correct Answer: B Difficult Level: 3 13. (a+b+c)​2​​ Which of the following is equivalent to the above expression? A. a​2​​+b​2​​+c​2​​+2(ab+bc+ca) B. a​2​​+b​2​​+c​2​​ C. a​2​​+2abc+c​2​​ D. a​2​​+2ab+b​2​​+2bc+c​2​​ ​​ Correct Answer: A Difficult Level: 3 14. xya+x2y2b Which of the following is equivalent to the above expression? A. xy(b-axy)ab B.xy( xyb-1a) C. ( xya-1b)yx D. xy(a-bxy)ab ​​ Correct Answer: A Difficult Level: 3 15. m+n4-4m+n=(x-4)(x+4)4(m+n) Which of the following is equivalent to x if the above equation is true for all m≠n? A. m-n B. m+n C. m-n D. m+n ​​ Correct Answer: D Difficult Level: 4 16. (yt)​6t​​−(lv)​8v​​ Which of the following is equivalent to the above expression? A. y​6​​t​t​​−l​8​​v​v​​ B. v​8v​​l​8v​​−t​6t​​y​6t​​ C. ((lv)​4v​​+(yt)​3t​​)((lv)​4v​​−(yt)​3t​​) D. ((vl)​v4​​+(ty)​t3​​)((ty)​t3​​−(vl)​v4​​) ​​ Correct Answer: D Difficult Level: 4 17. (y​2​​−32y+256−k)(y​2​​−32y+256+k)=(y−16)​4​​−100 What is the value of k​2​​ in the above equation? Correct Answer: 100 Difficult Level: 4 18. (a​m​​)​n​​⋅a​mn​​ Which of the following is equivalent to the above expression? A. 2a​mn B. a​2mn C.am2n2 D.​​ amn+mn ​​ Correct Answer: B Difficult Level: 4 19. s​3​​t​3​​+1 Which of the following is equivalent to the above expression? A. (st−1)(s​2​​t​2​​+st+1) B. (st−1)((st)​2​​−st+1) C. (st+1)(s​2​​t​2​​+st+1) D. (st+1)((st)​2​​−st+1) ​​ Correct Answer: D Difficult Level: 4 20. If 2​m​​=x and 7 ​n​​=y, then which of the following is equivalent to 784​mn​​? A. x​2m​​⋅y​4n​​ B. x​2n​​⋅y​4m​​ C. x​4m​​⋅y​2n​​ D. x​4n​​⋅y​2m ​​ Correct Answer: D Difficult Level: 4 21. p+77-p-77 Which of the following is equivalent to the above expression? A. p-p7 B. p+p7 C. 7+77 D. 7-77 ​​ Correct Answer: C Difficult Level: 4 22. x2-2x-8x+3·x+2x+3 Which of the following is equivalent to the above expression for x≠−3? A. 2(x-4)(x+2)3(x+3) B. (x-4)(x+2)2x+3 C. (x-4)(x+2)2x2+6x+9 D. 2(x-4)(x+2)x2+6x+9 ​​ Correct Answer: C Difficult Level: 4 23. (w-32)(w+72) Which of the following is equivalent to the above expression? A.(w-3)(w+7)2 B. (2w+7)(2w-3)2 C. (w-3)(w+7)4 D. (2w+7)(2w-3)4 ​​ Correct Answer: D Difficult Level: 4 24. c(ax−b)−d(b−ax) Which of the following is equivalent to the above expression? A. (ax−b)(c+d) B. (ax−b)​2​​(c+d) C. (b−ax)​2​​(c−d) D. (ax−b)(b−ax)(c−d) ​​ Correct Answer: A Difficult Level: 4 25. (u+t)​3​​ Which of the following is equivalent to the above expression? A. u​3​​+3ut+t​3​​ B. u​3​​+3ut(u+t)+t​3​​ C. u​3​​+6ut+t​3​​ D. u​3​​+6u​2​​t+6ut​2​​+t​3​​ ​​ Correct Answer: B Difficult Level: 4 26. a+bc-d-a+bd-c Which of the following is equivalent to the above expression for c≠d? A. 0 B. 2bc-d C. 2(a+b)c-d D. 2a+2b2c-2d ​​ Correct Answer: C Difficult Level: 4 27. If x​3​​+b​3​​=(x+b)(x​2​​−xb+9), what is a possible value of b? Correct Answer: 3或-3 Difficult Level: 2 28. a​2​​x−3a​2​​+2x−6 Which of the following is equivalent to the above expression? A. (a​2​​)(x−3)−2(x+3) B. (ax+3)(a−2) C. (x+3)(a​2​​−2) D. (x−3)(a​2​​+2) ​​ Correct Answer: D Difficult Level: 4