Multiplying brackets

• (p+5)2 = p2 +10p+25

  
• = n2 - 11n +30

  
• The identity of 8 – 2(𝒏 – 1) is 10 – 2𝒏

  The constant 8 is a separate term. 

  The terms in the bracket are multiplied by – 2

  The expression is now 8 – 2𝒏 + 2, this can be simplified by collecting the like terms (8 + 2 = 10).   

  8 – 2(𝒏 – 1) is equivalent to 10 – 2𝒏. The expressions are identities. 
• The correct identity is 𝒏 + 4

  Expand each bracket in the expression. 

  Multiply each term in the bracket by the term attached to the front of the bracket.

  For the first bracket, 2 is multiplied by 2�� and –1  

  For the second bracket, –3 is multiplied by 𝒏 and –2

  The expression is now 4𝒏 – 2 – 3𝒏 + 6.  This expression can be simplified by collecting the like terms:

  4𝒏 – 3𝒏 = 𝒏 and 6 – 2 = 4

  2(2𝒏 – 1) – 3(𝒏 – 2) is equivalent to 𝒏 + 4. They are identities.