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I hate to ask it…. How do we multiply and divide these things?. 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. - PowerPoint PPT PresentationTRANSCRIPT
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I hate to ask it…I hate to ask it…
How do we multiply and divide these things?
How do we multiply and divide these things?
![Page 2: I hate to ask it…](https://reader035.vdocuments.net/reader035/viewer/2022072013/56812aad550346895d8e740c/html5/thumbnails/2.jpg)
Before we beginBefore 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
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
![Page 3: I hate to ask it…](https://reader035.vdocuments.net/reader035/viewer/2022072013/56812aad550346895d8e740c/html5/thumbnails/3.jpg)
Multiplying binomialsMultiplying 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
(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
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Important casesImportant cases
Squaring binomial (x+y)(x+y)=(x+y)2
=x2+2xy+y2
Conjugates (x+y)(x–y)=x2-xy+xy-y2
x2-y2
Squaring binomial (x+y)(x+y)=(x+y)2
=x2+2xy+y2
Conjugates (x+y)(x–y)=x2-xy+xy-y2
x2-y2
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Treat complex numbers like binomials, ¡que facil!
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!
(3-6i)*2i =3*2i–6i*2i =6i-12i2
=12+6i You need to remember to simplify the i and
combine like terms!
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ExamplesExamples