Chapter 8

• What is the result of expanding the brackets in the expression \((x+3)(x^2-x-2)\)?


  x³ - x² - 12x - 6
• How do you expand the expression \((2x+3)(x+2)(x-1)\)?


  First expand \((2x+3)(x+2)\) then multiply the result by \((x-1)\)
• What is the final result of expanding \((2x+3)(x+2)(x-1)\)?


  2x³ + 3x² + x - 6
• What is the result of the expression \(8p^2(3-4p)-6p(2p+4)\) after simplification?


  • 32p³ + 12p² - 24p
• What is the difference of squares formula as shown in the example \((x+4)(x-4)\)?


  It simplifies to \(x^2 - 16\)
• What is the result of the expression \((x+5)(x-5)\)?


  x² - 25
• What are the steps to factor the expression \((a+b)^2 + b(a-b)\)?


  1. Start with \((a+b)^2 + b(a-b)\)
  2. Expand to get \((a+b)^2 + ba - b^2\)
  3. Factor out \((a+b)^2\) and simplify
  4. Result: \((a+b)^2 (x^2 - 2b)\)
• How do you solve the quadratic equation \(ax^2 + bx + c = 0\) using the ac method? Give an example.


  For \(2x^2 - 2x - 3 = 0\), calculate \(ac = 2 \times -3 = -6\)
• What is the result of factoring \(2x^2 - 2x - 3 = 0\) using the ac method?


  (x-1)(2x+3)
• What is the standard form of a quadratic equation?


  ax² + bx + c = 0
• How do you rearrange the equation \(y^2 = 2x + 2\) to make \(x\) the subject?


  x = \frac{y^2 - 2}{2}
• What is the rearranged form of \(y^2 = 7x + 12\) to isolate \(x\)?


  x = \frac{y^2 - 12}{7}
• How do you isolate \(x\) in the equation \(y = \sqrt{2x + 1}\)?


  Square both sides to get \(y^2 = 2x + 1\)
• What is the rearranged form of \(y = 2x^2 - 4\) to isolate \(x\)?


  log y = log(2x^2 - 4)
• How do you isolate \(x\) in the equation \(y = \frac{\sqrt{x}}{x^2}\)?


  x = y^2
• What is the method to isolate \(x\) when it appears more than once in an equation?


  Combine like terms on one side and isolate \(x\)
• How do you solve the equation \(2x + x = 6\)?


  x = 1
• What is the rearranged form of \(y = 3x + 1\) to isolate \(x\)?


  x = \frac{1}{2y - 1}
• What are the methods to solve quadratic equations?


  1. Factorization
  2. Completing the square
  3. Quadratic formula
  4. Graphing