Algebraic expressions

• What do letters in algebra represent?


  They stand for values that can change (variables) or values that are not known (unknown).
• What is a term in algebra?


  A term is a number or letter on its own or a number/letter multiplied together.
• What is an expression in algebra?


  An expression is a set of terms combined using +, -, *, or ×.
• What is an identity in algebra?


  An identity is a statement that is true no matter the values chosen.
• If a teacher buys x packs of pens and b boxes of rulers, what is the expression for the total number of pens and rulers bought?


  The expression is $6x +$$10b$.
• What is the process of simplifying expressions by collecting like terms?


  • Combine terms with the same variable.
  • Example: $5a +$$2b +$$3a - 6b =$$(5a + 3a) +$$(2b - 6b) =$$8a - 4b$
• What is the simplified form of $b +$$b +$$b +$$b$?


  The simplified form is $4b$.
• What is the simplified form of $5m +$$3m - 2m$?


  The simplified form is $6m$.
• How can algebraic expressions be manipulated?


  • They can be added and subtracted.
  • They can also be multiplied and divided.
• What is the simplified form of $axa$?


  The simplified form is $a^2$.
• What is the simplified form of $bxbxb$?


  The simplified form is $b^3$.
• What does squaring a number or letter mean?


  It means multiplying the number or letter by itself.
• What does the index or power number indicate in an expression like $a^2$?


  It tells us how many times a number or letter has been multiplied by itself.
• What is the result of $a^2 \times a^3$?


  The result is $a^5$.
• What is the process of expanding brackets in algebra?


  • Multiply each term inside the bracket by the term outside.
  • Example: $3(m+7) =$$3m +$$21$
• What is the expanded form of $(y+2)(y+3)$?


  The expanded form is $y^2 +$$5y +$$6$.
• What does FOIL stand for in expanding brackets?


  FOIL stands for First, Outer, Inner, Last terms in the brackets.
• What is the result of expanding $(y+z)(y+3)$?


  The result is $y^2 +$$3y +$$zy +$$3z$.
• What is factorization in algebra?


  • Factorization is the reverse process of expanding brackets.
  • It involves taking out the highest common factor (HCF) of all terms.
• What is the factorization of $6x +$$9$?


  The factorization is $3(2x + 3)$.
• What is the HCF of 6 and 9?


  The HCF of 6 and 9 is 3.
• What are the rules for adding and multiplying even and odd numbers?

  • Even + Even = Even
  • Even × Even = Even
  • Odd + Odd = Even
  • Even + Odd = Odd
  • Odd × Even = Even
• How can algebra be used in expressions?


  Algebra can show relationships when different expressions are equivalent.