2.1.3 Expanding products of binomials

• Match the binomial with its terms:

  \(x + 3\) ↔️ \(x\), \(3\)

  \(2y - 5\) ↔️ \(2y\), \(-5\)

  \(a + b\) ↔️ \(a\), \(b\)
• What is the result of multiplying the last terms in \((x + 4)(y - 2)\)?

  -8
• Steps to combine like terms

  1️⃣ Identify like terms

  2️⃣ Add or subtract coefficients

  3️⃣ Write the result
• Like terms must have the same variable but can have different exponents

  False
• What is a binomial in algebra?

  Two-term algebraic expression
• The final term in the expansion of \((x + 2)(y + 3)\) is 6.


  True
• Expanding a product of binomials involves multiplying each term in the first binomial by each term in the second binomial.


  True
• Combining the terms after expanding \((x + 4)(y - 2)\) results in \(xy - 2x + 4y - 8\).


  True
• What is the expanded form of \((x + 2)(y + 3)\)?

  xy + 3x + 2y + 6
• What is the result of distributing \(2\) in \((x + 2)(y + 3)\)?

  2y + 6
• What is the simplified form of \(3x + 5x - 2y\)?

  8x - 2y
• What is the product of the first terms in \((a + 2)(b - 3)\)?

  $ab$
• A binomial can only include variables with coefficients.

  False
• Where are binomials commonly used in mathematics?

  Solving equations
• What does it mean to expand a product of binomials?

  Distributing terms
• Which terms are multiplied when finding the last terms of two binomials?

  Last and last terms
• Steps to multiply terms within parentheses using the distributive property

  1️⃣ Apply the Distributive Property

  2️⃣ Multiply the First Terms

  3️⃣ Multiply the Outer Terms

  4️⃣ Multiply the Inner Terms

  5️⃣ Multiply the Last Terms
• The inner terms are multiplied by multiplying the second term of the first binomial with the first term of the second binomial.


  True
• What property is used to expand products of binomials?

  Distributive property
• Steps to expand \((x + 2)(y + 3)\)

  1️⃣ Distribute \(x\)

  2️⃣ Distribute \(2\)

  3️⃣ Combine distributed terms
• What term is produced when \(x\) is multiplied by \(y\) in the expansion of \((x + 2)(y + 3)\)?

  xy
• The first step in expanding binomial products is to multiply the first terms of both binomials.


  True
• Multiplying the outer terms involves multiplying the first term of the first binomial with the last term of the second binomial.


  True
• Expand \((a + 6)(a - 3)\)

  a^2 + 3a - 18
• Combining like terms in \(2x + 5x\) results in \(7x\).


  True
• The expanded form of \((a + 2)(b - 3)\) is $ab - 3a +$$2b - 6$


  True
• Steps to combine like terms in an algebraic expression

  1️⃣ Identify like terms

  2️⃣ Combine coefficients of like terms

  3️⃣ Rearrange terms from highest to lowest power
• What is the result of multiplying the first terms in \((x + 4)(y - 2)\)?


  xy
• What is the product of the inner terms in \((a + 2)(b - 3)\)?

  $2b$
• What is multiplied when finding the outer terms of two binomials?

  First and last terms
• The outer terms in \((x + 4)(y - 2)\) multiply to -2x.


  True
• What property is used to multiply terms within parentheses?

  Distributive Property
• What does the FOIL method stand for in expanding binomial products?

  First, Outer, Inner, Last
• The simplified expansion of \((y - 4)(y + 2)\) is \(y^2 - 2y - 8\)


  True
• What are the like terms in the expression \(2x + 3 + 5x - 1\)?

  \(2x\) and \(5x\), \(3\) and \(-1\)
• Steps to expand \((y - 4)(y + 2)\) using the FOIL method

  1️⃣ Multiply the First terms: \(y \times y = y^2\)

  2️⃣ Multiply the Outer terms: \(y \times 2 = 2y\)

  3️⃣ Multiply the Inner terms: \(-4 \times y = -4y\)

  4️⃣ Multiply the Last terms: \(-4 \times 2 = -8\)

  5️⃣ Combine like terms: \(y^2 + 2y - 4y - 8\)

  6️⃣ Simplify: \(y^2 - 2y - 8\)
• The simplified expansion of \((2x + 3)(x - 5)\) is \(2x^2 - 7x - 15\)

  True
• Steps to expand \((2x + 3)(x - 5)\) using the FOIL method

  1️⃣ Multiply the First terms: \(2x \times x = 2x^2\)

  2️⃣ Multiply the Outer terms: \(2x \times -5 = -10x\)

  3️⃣ Multiply the Inner terms: \(3 \times x = 3x\)

  4️⃣ Multiply the Last terms: \(3 \times -5 = -15\)

  5️⃣ Combine like terms: \(2x^2 - 10x + 3x - 15\)

  6️⃣ Simplify: \(2x^2 - 7x - 15\)
• The simplified expansion of \((3b - 1)(b + 4)\) is \(3b^2 + 11b - 4\)

  True
• Steps to expand products of binomials using the distributive property

  1️⃣ Multiply the first terms

  2️⃣ Multiply the outer terms

  3️⃣ Multiply the inner terms

  4️⃣ Multiply the last terms

  5️⃣ Combine the results