Q5.68

Question

Choose the appropriate pattern and use it to find product:

$(a) {(6 x + 7)}^{2} (b) (3 x - 4) (3 x + 4) (c) (2 x - 5) (5 x - 2) (d) {(6 n - 1)}^{2}$

Step-by-Step Solution

Verified

Answer

$M u l t i p l y t h e p o l y n o m i a l s (a) {(6 x)}^{2} + 7^{2} + 2 \times 6 x \times 7 36 x^{2} + 49 + 84 x (b) 3 x \times 3 x + 3 x \times 4 - 4 \times 3 x - 4 \times 4 9 x^{2} - 16 (c) 2 x \times 5 x - 2 x \times 2 - 5 \times 5 x + 5 \times 2 10 x^{2} - 29 x + 10 (d) {(6 n)}^{2} + 1 - 2 \times 6 n \times 1 36 n^{2} + 1 - 12 n$

1Step 1

$G i v e n i n f o r m a t i o n : (a) {(6 x + 7)}^{2} (b) (3 x - 4) (3 x + 4) (c) (2 x - 5) (5 x - 2) (d) {(6 n - 1)}^{2}$

2Step 2

Conjugate Pair

A conjugate pair is two binomials of the form

(a−b),(a+b).(a−b),(a+b).

The pair of binomials each have the same first term and the same last term, but one binomial is a sum and the other is a difference.

3Part (a) Step 1. Multiply the binomials

We are asked to square a binomial.it fits the binomial squares pattern.

${(6 x + 7)}^{2} U s e t h e p a t t e r n 6 x^{2} + 2.6 x . 7 + {(7)}^{2} S i m p l i f y 6 x^{2} + 84 x + 49$

4Part(b) Step1. Multiply the binomials

$(b) T h e s e a r e c o n j u g a t e s . T h e y h a v e t h e s a m e f i r s t n u m b e r s a n d s a m e l a s t n u m b e r s, a n d o n e b i n o m i a l i s a s u m a n d o t h e r i s a d i f f e r e n c e . I t f i t s t h e p r o d u c t o f c o n j u g a t e p a t t e r n s . (3 x - 4) (3 x + 4) U s e t h e P a t t e r n {(3 x)}^{2} - {(4)}^{2} S i m p l i f y 3 x^{2} - 16$

5Part(c) Step1. Multiply the binomials

$(c) (2 x - 5) (5 x - 2) T h i s p r o d u c t d o e s n o t f i t t h e p a t t e r n s, s o w e w i l l u s e t h e F O I L . U s e F O I L 10 x^{2} - 4 x - 25 x + 10 S i m p l i f y 10 x^{2} - 29 x + 10$

6Part(b) Step1. Multiply the binomials

$(d) {(6 n - 1)}^{2} A g a i n, w e w i l l s q u a r e a b i n o m i a l s o w e u s e t h e b i n o m i a l s q u a r e s p a t t e r n U s e t h e p a t t e r n {(6 n)}^{2} - 2.6 n . 1 + 1^{2} S i m p l i f y 6 n^{2} - 12 n + 1$

Q5.67

Q5.69

Other exercises in this chapter

Q5.66

Multiply: (a) (2x+7)(2x-7)(b) (3x-y)(3x+y)

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Q5.67

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Q5.69

For function f(x)=x-5 and g(x)=x2-2x+3 , Find (a) (f.g)(x) (

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Q. 5.70

For function fx=x-7 and gx=x2+8x+4. Find (a) f·gx (b) f·g2

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