8.3 MULTIPLYING BINOMIALS:

Distributive Property: for any real numbers a, b, c, and d:

(a+b)(c+d)= ac +bd +ad+bc

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

GOAL:

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)?

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

MULTIPLYING BINOMIALS:We can also use a table to:

2x 43x-7

6x2 12x-14x -28

6x2+12x-14x-286x2-2x-28

REAL-WORLD:

What is the area of the frame?

5x-2

7x+1

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

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?

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

VIDEOS:PolynomialsMultiplying

Multiplying:

https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/polynomial_tutorial/v/multiplying-polynomials

CLASSWORK:

Page 489-490:

Problems: As many as needed to master the concept