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Mastering Multiplication and Division of Binomials and Complex Numbers

This guide dives into the multiplication and division of binomials, highlighting key concepts like FOIL (First, Outer, Inner, Last) for binomial multiplication. We explore examples of multiplying binomials (e.g., (x+3)(x-5)) and illustrate how to simplify terms. Additionally, we discuss special cases such as squaring a binomial and working with conjugates. The tutorial also covers treating complex numbers as binomials, showcasing examples involving imaginary units. Understanding these principles is essential for effective algebraic manipulation.

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Mastering Multiplication and Division of Binomials and Complex Numbers

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Presentation Transcript

  1. I hate to ask it… How do we multiply and divide these things?

  2. Before we begin • Remember multiplying binomials? • (Binomials are things with two terms) • Ex. (x – 2), (y + 7), (3 + 5z) • To multiply two binomials, we had to multiply each part of each binomial • FOIL • First, Outer, Inner, Last

  3. Multiplying binomials • (x+3)(x-5) • Multiply first terms: x*x=x2 • Multiply outer terms: x*(-5)=-5x • Multiply inner terms: 3*x=3x • Multiply last terms: 3*(-5)=-15 • Add them all together: x2-5x+3x-15 • Combine like terms: x2-2x-15

  4. Important cases • Squaring binomial • (x+y)(x+y)=(x+y)2 • =x2+2xy+y2 • Conjugates • (x+y)(x–y)=x2-xy+xy-y2 • x2-y2

  5. Treat complex numbers like binomials, ¡que facil! • (3-6i)*2i • =3*2i–6i*2i • =6i-12i2 • =12+6i • You need to remember to simplify the i and combine like terms!

  6. Examples

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