Algebra Pointers

• Algebraic expression


  A combination of numbers and letters with signs of operations and/or grouping symbols
• Algebraic expressions


  • 2a+2b+5
  • 4x³-9x²+8
  • 1/5x-2y³
  • √√3xy
  • √b2-4ac
• Constant


  A symbol that does not change its value in a particular problem or discussion, usually represented by a number symbol
• Variable


  A symbol that may change its value in a particular problem or discussion, usually represented by a letter
• Terms


  The smaller parts of an algebraic expression separated by + and - signs
• Like terms


  Terms having identical literal parts
• Unlike terms


  Terms having different literal parts
• Factors


  The numbers and letters that are multiplied to give a product
• Numerical coefficient


  A coefficient that is not a variable
• Literal coefficient


  A coefficient that is expressed by a variable/letter or product of variables
• Polynomial


  An algebraic expression having only terms of the form ax^n, where a is any real number and n is a whole number
• Monomial


  A polynomial of one term
• Binomial


  A polynomial of two unlike terms
• Trinomial


  A polynomial of three unlike terms
• Polynomials never have variables in the denominator
• Degree of a term

  The sum of the exponents of its variables
• Degree of a polynomial

  The same as that of its highest-degree term
• Standard form


  A polynomial written with its exponents arranged in descending order
• Removing grouping symbols


  1. If preceded by +, copy terms inside

  2. If preceded by -, change sign of each enclosed term

  3. Start with innermost set and finish with outermost set
• Adding and subtracting algebraic expressions

  1. Use grouping symbols, remove them, and combine like terms

  2. Arrange in columns, rearrange terms so similar terms are in same column, then add or subtract by column
• Laws on exponents


  • a^m * a^n = a^(m+n)
  • a^m / a^n = a^(m-n)
  • a^0 = 1
  • a^(-n) = 1/a^n
• Avoid mistakes like multiplying/dividing exponents, adding exponents, misreading parentheses, etc.
• Simplifying expressions with exponents

  Apply exponent laws, express answers with only positive exponents
• Multiplying and dividing algebraic expressions

  Use distributive property, combine like terms
• add exponents.
• Commutative axiom


  Allows rearranging of terms in addition and multiplication
• Squaring a trinomial


  1. Square each term

  2. Get twice the product of each of the 3 pairs of terms
• Squaring a trinomial


  • (x + y + z)²
  • (x-y-2)²
  • (a-2b+3)²
• Cubing a binomial


  1. Cube the first term

  2. Cube the second term
• Cubing a binomial


  • (a+b)
  • (a-b)
• Product of a binomial and a trinomial

  1. Cube the first term of the binomial

  2. Cube the second term of the binomial
• Product of a binomial and a trinomial


  • (x+y)(x²-xy+ y²)
  • (x − y)(x² + xy + y²)
  • (2+m)(4-2m+m²)
  • (m-2)(m² + 2m+4)
  • (-2-m)(4-2m+m²)
• Factoring


  Rewriting an expression in completely factored form, where each factor is prime
• Common monomial factoring


  Factor out the common monomial
• Common monomial factoring


  • 3x³-15x³
  • -3x²-6x+3
  • 4m'n-7m²n²
  • -15x²+10x
  • 6x-15x+3x²
• Common binomial factoring


  Factor out the common binomial
• Common binomial factoring


  • 4(x-y)-(x-y)
  • n(n-3)-7(3-n)
  • -a5b-4a2b2+5a³b³
• Factoring sum/difference of two cubes

  1. Cube the first term

  2. Cube the second term
• Factoring sum/difference of two cubes

  • x²+64
  • 125+(x+1)³
  • 8r³-27s³
• Factoring perfect square trinomials

  1. Factor as (a+b)²

  2. Factor as (a-b)²