jM g n ^
How can a diagram
help you m ultiply
tw o binomials?
Draw arrows from each
term of the first binomial
to each term of the
second binomial. This will
help you organize the
products of the terms.
How can you simplify
(x+ 1)2?
Write the expression
as ( x + 1 ) ( x + 1)
and multiply the
binomials. You do
not "distribute" the
exponent to each term:
(x+ 1)2 + x 2 + 12.Using FOIL
What is a simpler form of (5x — 3)(2x +1)?(5x - 3)(2x + 1)The p ro d u ct is 10x2 - x - 3.First Outer Inner Last
(5x)(2x) + (5x)(l) + (—3)(2x) + (-3X1)
10x2 + 5x - 6x 3
10x2 - X 3£ Goflt? 3. W hat is a sim pler form of each product? Use th e FOIL m ethod.
a. (3x - 4)(x + 2) b. {n - 6)(4n - 7) c. (2p1 + 3)(2p - 5)Pr o b l em 4 Applying Multiplication of Binomials
Multiple Choice A cylinder has the dimensions shown in the
diagram. Which polynomial in standard form best describes the
total surface area of the cylinder?C£) 2-7TX2 + 4-7TX + 277 CO 477X2 + 14l7X + 1077
CID 277X2 + 1077X + 877 C O 277X2 + 277X + 107T
The total surface area (S.A.) of a cylinder is given by the form ula
S. A. = 2vr2 + 2vrh, where r is th e radius of th e cylinder an d h is th e height.
S.A. = 27r r 2 + 2irrh
= 27t(x + l)2 + 27t(x + l)(x + 4)
= 277(x + l)(x + 1) + 2t7(x + l)(x + 4)
= 277 (x 2 + x + x + l ) + 277 (x2 + 4x + X + 4 )
= 277(x2 + 2x+ 1 ) + 277(x2 + 5x + 4)
= 277 (x 2 + 2x + 1 + x2 + 5x + 4 )
= 277(2x2 + 7x + 5 )
= 477X2 + 1477X + 1077
The correct answ er is C.Surface area of a cylinder
Substitute x + 1 f o r r and x + 4 for h.
Write (x + 1)2 as ( x + 1)(x + 1).
Multiply binomials.
Combine like terms.
Factor out 277.
Combine like terms.
Write in standard form.Got It? 4. W hat is th e total surface area of a cylinder w ith radius x + 2 an d height
x + 4? Write your answ er as a polynom ial in stan d ard form.You can use the FOIL m eth o d w hen you m ultiply two binom ials, b u t it is n o t helpful
w hen m ultiplying a trinom ial an d a binom ial. In this case, you can use a vertical
m eth o d to distribute each term.500 Ch ap t er 8 Polyn om i al s and Factoring