Q5.67 Choose the appropriate pattern a... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q5.67 (page 534)

Choose the appropriate pattern and use it to find product:
$(a) (9 b - 2) (2 b + 9) (b) {(9 p - 4)}^{2} (c) {(7 y + 1)}^{2} (d) (4 r - 3) (4 r + 3)$

Short Answer

Expert verified

$M u l t i p l y t h e b i n o m i a l s, w e g e t (a) 9 b 脳 2 b + 9 b 脳 9 - 2 脳 2 b - 2 脳 9 18 b^{2} + 77 b - 18 (b) {(9 p)}^{2} + {(4)}^{2} - 2 脳 9 p 脳 4 81 p^{2} + 16 - 72 p (c) {(7 y)}^{2} + 1 + 2 脳 7 y 脳 1 49 y^{2} + 1 + 14 y (d) 4 r 脳 4 r + 4 r 脳 3 - 3 脳 4 r - 3 脳 3$

Step by step solution

Step 1

$G i v e n I n f o r m a t i o n (a) (9 b - 2) (2 b + 9) (b) {(9 p - 4)}^{2} (c) {(7 y + 1)}^{2} (d) (4 r - 3) (4 r + 3)$

Step 2

$A b i n o m i a l c o n j u g a t e i s f o u n d s i m p l y b y c h a n g i n g t h e s i g n o f t h e 2 n d t e r m . T h e b i n o m i a l c o n j u g a t e o f (a + b) i s (a - b) . V e r t i c a l a d d i t i o n i s a m e t h o d o f a d d i n g w h e r e t h e n u m b e r s a r e l i n e d u p i n T h e m n e m o n i c F O I L t e l l s u s e x a c t l y w h a t t e r m s t o m u l t i p l y, a n d i n w h a t o r d e r : F i r s t 鈥� m u l t i p l y t h e f i r s t t e r m s O u t s i d e 鈥� m u l t i p l y t h e o u t s i d e / o u t e r t e r m s I n s i d e 鈥� m u l t i p l y t h e i n s i d e / i n n e r t e r m s L a s t 鈥� m u l t i p l y t h e l a s t t e r m s c o l u m n s a c c o r d i n g t o t h e i r p l a c e s v a l u e .$

Part(a) Step1. Use FOIL method.

$(a) (9 b - 2) (2 b + 9) U s e F O I L 9 b 脳 2 b + 9 b 脳 9 - 2 脳 2 b - 2 脳 9 S i m p l i f y 18 b^{2} + 77 b - 18$

Part(b) Step1. We are asked to square a binomial. It fits the binomial square pattern.

$(b) U s e p a t t e r n {(9 p)}^{2} + {(4)}^{2} - 2 脳 9 p 脳 4 S i m p l i f y 81 p^{2} + 16 - 72 p$

Part(c) Step1. Again binomial square pattern.

$(c) U s e p a t t e r n {(7 y)}^{2} + {(1)}^{2} + 2 脳 7 y 脳 1 S i m p l i f y 49 y^{2} + 1 + 14 y$

Part(d) Step1. If fits the product of conjugate pattern.

$(d) U s e p a t t e r n {(4 r)}^{2} - {(3)}^{2} S i m p l i f y 16 r^{2} - 9$

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91影视

Choose the appropriate pattern and use it to find product:
$(a) (9 b - 2) (2 b + 9) (b) {(9 p - 4)}^{2} (c) {(7 y + 1)}^{2} (d) (4 r - 3) (4 r + 3)$

Short Answer

Step by step solution

Step 1

Step 2

Part(a) Step1. Use FOIL method.

Part(b) Step1. We are asked to square a binomial. It fits the binomial square pattern.

Part(c) Step1. Again binomial square pattern.

Part(d) Step1. If fits the product of conjugate pattern.

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91影视

Choose the appropriate pattern and use it to find product:(a)(9b-2)(2b+9)(b)(9p-4)2(c)(7y+1)2(d)(4r-3)(4r+3)

Short Answer

Step by step solution

Step 1

Step 2

Part(a) Step1. Use FOIL method.

Part(b) Step1. We are asked to square a binomial. It fits the binomial square pattern.

Part(c) Step1. Again binomial square pattern.

Part(d) Step1. If fits the product of conjugate pattern.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Choose the appropriate pattern and use it to find product:
$(a) (9 b - 2) (2 b + 9) (b) {(9 p - 4)}^{2} (c) {(7 y + 1)}^{2} (d) (4 r - 3) (4 r + 3)$