PRODUTOS NOTÁVEIS (EXERCÍCIOS) 🔺TÓPICOS EM ÁLGEBRA (MÓDULO 2)

NOTABLE PRODUCTS (EXERCISES) This is the second video (second module) of the Topics in Algebra course. In it, I work with a list of 10 exercises that you can download here: Lesson PDF: https://drive.google.com/open?id=1nqJ... Also watch the previous video:    • PRODUTOS NOTÁVEIS 🔺TÓPICOS EM ÁLGEBRA (MÓD...   1. Expanding (11a+9b)^2-(11a+9b).(11a-9b) We get: (A) 198ab+162b² (B) 198ab-162b² (C) 162b^2-198ab (D) 198ab (E) -198ab 2. If m is a perfect square, then the expression for the perfect square immediately above m is: (A) m² + 1 (B) √m+1 (C) m²+2m+1 (D) m^2-1 (E) m+2√m+1 3. The solution to the equation: (〖10〗^12+25)^2-(〖10〗^12-25)^2=〖10〗^x Is: (A) 10 (B) 12 (C) 14 (D) 25 (E) 50 4. The value of the product: (√5+√6+√7).(√5+√6-√7).(√5-√6+√7).(-√5+√6+√7) Is equal to (A) 100 (B) 101 (C) 102 (D) 103 (E) 104 5. Calculating (x+1)^2+(x-1)^2+2(x+1).(x-1) We get: (A) 4x²+1 (B) 4x²-1 (C) 3x²+1 (D) 3x²-1 (E) 4x² 6. In the identity (1+x+x^2 )^2=Ax^4+Bx^3+Cx^2+Dx+E The sum A+C+E is equal to (A) 9 (B) 7 (C) 6 (D) 5 (E) 2.5 7. Given M= (x+1/x)^2 and N= (x-1/x)^2 The value of (M+N)² is (A) 4x^2+ 4⁄x² (B) 4x^4+ 4⁄x^4 (C) 4x^4+8+ 4⁄x^4 (D) 4x^2+8+ 4⁄x² (E) 4x^4-8+ 4⁄x^4 8. The product of the sum and the difference of two terms is equal to 4x²-81y². The product of these two terms is: (A) 18x²y² (B) 36xy (C) 32x³y³ (D) 18xy (E) 36x²y² 9. If A=(3^x+3^(-x))/2 and B=(3^x-3^(-x))/2 Then for all real x, we have A²-B² equals: (A) -2 (B) -1 (C) 0 (D) 1 (E) 2 10. One of the factors of the expression (x+y+z)^3-x^3-y^3-z³ is: (A) 2(x+y) (B) 3(x-z) (C) 3(y+z) (D) 2(y+z) (E) 6(x+y)