8.3 multiplying binomials: distributive property: for any real numbers a, b, c, and d: (a+b)(c+d)=...
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8.3 MULTIPLYING BINOMIALS:
Distributive Property: for any real numbers a, b, c, and d:
(a+b)(c+d)= ac +bd +ad+bc
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8.3 MULTIPLYING BINOMIALS:
FOIL METHOD: for any real numbers a, b, c, and d in (a+b)(c+d):
FIRST: (a)(c) = acOUTER: (a)(d) = adINNER: (b)(c) = bcLAST: (b)(d) = bd
= ac+ad+bc+bd
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GOAL:
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MULTIPLYING BINOMIALS:When multiplying polynomials we must keep in mind the laws of exponents from chapter 7 and the distributive property.Ex:
What is the simplest form of:
(2x+4)(3x– 7)?
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FOIL METHOD:
FIRST: (2x)(3x) = 6x2
OUTER: (2x)(-7) = -14xINNER: (4)(3x) = 12xLAST: (4)(-7) = -28
(2x+4)(3x– 7)?
6x2-14x+12x-28
6x2-2x-28
The simplest form is: 6x2-2x-28
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MULTIPLYING BINOMIALS:We can also use a table to:
2x 43x-7
6x2 12x-14x -28
6x2+12x-14x-286x2-2x-28
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REAL-WORLD:
What is the area of the frame?
5x-2
7x+1
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SOLUTION:Using the FOIL method, table or distributive property:
5x-2
7x+1
Area = b.h
Area = (7x+1)(5x-2)
Area = 35x2-14x+5x-2
Total area = 35x2-9x-2
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REAL-WORLD:
A factory is looking into making the new label of a can of soup.The can needs to have the dimensions shown in the sketch.what is the total amount of paper needed to make a label?
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SOLUTION:The label will need to be a rectangle, but the length of the label is the circumference of the can (2πr):
x + 4
Area = b.h Area = (2πx+2π)(x+4) Area = 2πx2+8xπ+2πx+8π
2πr =2π(x+1)=2πx+2π
Total paper needed = 2πx2+10xπ+8π
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VIDEOS:PolynomialsMultiplying
Multiplying:
https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/polynomial_tutorial/v/multiplying-polynomials
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CLASSWORK:
Page 489-490:
Problems: As many as needed to master the concept