Expanding brackets

• What is the process of expanding a single bracket?

  It involves multiplying the term outside the bracket by each term inside the bracket.
• What does the expression \(3x(x + 2)\) represent?

  It represents \(3x\) multiplied by the bracket \((x + 2)\).

  
• What are the terms outside and inside the bracket in the expression \(3x(x + 2)\)?


  The term outside is \(3x\) and the terms inside are \(x + 2\).

  
• How do you expand the expression \(3x(x + 2)\)?


  It expands to \(3x \times x + 3x \times 2\), which simplifies to \(3x^2 + 6x\).

  
• What is the result of expanding \(3x(x + 2)\)?

  It simplifies to \(3x^2 + 6x\).

  
• What should you be cautious about when expanding expressions with negative signs?

  You should remember the basic rules of multiplication with signs.
• What is the rule for multiplying two negative numbers?

  Negative times negative equals positive.
• What is the rule for multiplying a negative number by a positive number?

  Negative times positive equals negative.
• How do you expand \(4x(2x - 3)\)?

  Multiply \(4x\) by both terms inside the brackets to get \(8x^2 - 12x\).

  
• How do you expand \(-7x(4 - 5x)\)?

  Multiply \(-7x\) by both terms inside the brackets to get \(-28x + 35x^2\).

  
• What are the steps to simplify an expression with multiple terms in brackets?

  1. Expand each set of brackets separately.
  2. Collect like terms.
• How do you expand \(4(x + 7) + 5x(3 - x)\)?

  Expand to \(4x + 28 + 15x - 5x^2\).

  
• What is the final simplified form of \(4(x + 7) + 5x(3 - x)\)?

  It simplifies to \(19x + 28 - 5x^2\).

  
• How do you expand and simplify \(2(x + 5) + 3x(x - 8)\)?

  Expand to \(2x + 10 + 3x^2 - 24x\) and simplify to \(3x^2 - 22x + 10\).

  
• What is the FOIL method used for?

  • It is used to expand two brackets.
  • F = First terms
  • O = Outside terms
  • I = Inside terms
  • L = Last terms
• How do you expand \((x + 1)(x + 3)\) using the FOIL method?

  Multiply to get \(x^2 + 3x + x + 3\) and simplify to \(x^2 + 4x + 3\).

  
• What is the grid method for expanding brackets?

  It involves writing the brackets as headings in a grid and multiplying the terms in the rows and columns.
• How do you expand \((x + 1)(x + 3)\) using a grid?

  Write the brackets as headings, multiply each cell, and add the terms to get \(x^2 + 4x + 3\).
• How do you expand a bracket squared, such as \((x + 3)^2\)?

  Rewrite as \((x + 3)(x + 3)\) and use FOIL to get \(x^2 + 6x + 9\).
• What is the common mistake when expanding \((x + 3)^2\)?

  Stating that \((x + 3)^2\) is equal to \(x^2 + 3^2\).

  
• How do you expand \((2x - 3)(x + 4)\) using FOIL?

  Multiply to get \(2x^2 + 8x - 3x - 12\) and simplify to \(2x^2 + 5x - 12\).

  
• How do you expand \((x - 3)(3x - 5)\) using FOIL?

  Multiply to get \(3x^2 - 5x - 9x + 15\) and simplify to \(3x^2 - 14x + 15\).

  
• What are the steps to expand three brackets?

  1. Multiply out any two brackets and simplify.
  2. Replace the two brackets with one long bracket containing the expanded result.
  3. Expand this long bracket with the third bracket.

  
• How do you expand \((2x - 3)(x + 4)(3x - 1)\)?

  Start by expanding the first two brackets and then multiply by the third bracket.
• How do you simplify the expression after expanding three brackets?

  Collect like terms after expanding all brackets.
• How do you expand \((x - 3)(x + 2)(2x - 1)\)?

  Start by expanding the first two brackets and then multiply by the third bracket.
• What is the importance of keeping negative terms in brackets when expanding?

  It helps to avoid missing negative signs during multiplication.
• What is the final step after expanding and simplifying an expression with multiple brackets?

  Collect like terms to get the final simplified expression.