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3 years ago

Expand or factor each of the following expressions to determine which expressions are equivalent.

Mathematics

2 answers:

Leni [432]3 years ago

7 0

Answer:

The pair of equivalent expressions are 2 and 8, 3 and 7, 4 and 5.

Step-by-step explanation:

Expand or factor each of the following expressions

$(4x-3y)^2=(4x)^2-(2(4x)(3y)+(3y)^2$ $[\because (a-b)^2=a^2-2ab+b^2]$

$(4x-3y)^2=16x^2-24xy+9y^2$

$9x^2+3x-20=9x^2+15x-12x-20$

$9x^2+3x-20=3x(3x+5)-4(3x+5)$

$9x^2+3x-20=(3x+5)(3x-4)$

It is same as expression 8. Therefore expression 2 and 8 are equivalent.

$(3x-2)(9x^2+6x+4)=(3x-2)((3x)^2+(3x(2)+2^2)$

$(3x-2)(9x^2+6x+4)=(3x)^3-(2)^3$ $[\because a^3-b^3=(a-b)(a^2+ab+b^2)]$

$(3x-2)(9x^2+6x+4)=27x^3-8$

It is same as expression 7. Therefore expression 3 and 7 are equivalent.

$9x^2-24xy+16y^2=(3x)^2-2(3x)(4y)+(4y)^2$

$9x^2-24xy+16y^2=(3x-4y)^2$ $[\because (a-b)^2=a^2-2ab+b^2]$

It is same as expression 5. Therefore expression 4 and 5 are equivalent.

$(3x-4y)^2=9x^2-24xy+16y^2$

$(3x+2)(9x^2-6x+4)=(3x+2)((3x)^2-(3x(2)+2^2)$

$(3x+2)(9x^2-6x+4)=(3x)^3+(2)^3$ $[\because a^3+b^3=(a+b)(a^2-ab+b^2)]$

$(3x+2)(9x^2-6x+4)=27x^3+8$

$27x^3-8=(3x-2)(9x^2+6x+4)$

$(3x+5)(3x-4)=9x^2+3x-20$

Therefore the pair of equivalent expressions are 2 and 8, 3 and 7, 4 and 5.

bearhunter [10]3 years ago

4 0

(3x-4y)^2=9x^2-24x+16y^2
(3x-2)(9x^2+6x+4)=27x^3-8

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DATA SET 301

B1 B2

A1 38 60 39 47 44 38 45 30 36 22 20 27 22 44

A2 55 51 35 60 52 35 37 32 43 20 41 30 41 24

A3 63 40 50 58 64 60 64 25 46 23 20 42 41 35

DATA SET 302

B1 B2

A1 41 23 31 42 28 22 32 24 40 48 28 45 46 45

A2 33 29 27 42 24 49 26 44 47 46 41 27 47 46

A3 30 26 24 25 30 27 40 24 28 20 38 42 37 43

DATA SET 303

B1 B2

A1 40 36 50 37 62 59 53 47 37 33 37 20 35 21

A2 56 60 59 43 45 50 64 41 29 22 40 37 23 44

A3 59 56 62 41 37 63 51 46 30 48 21 26 28 23

DATA SET 304

B1 B2

A1 39 49 32 41 20 25 32 43 24 30 25 44 48 36

A2 45 21 45 46 27 24 45 37 36 23 32 23 38 26

A3 41 56 62 47 63 53 51 61 46 51 45 68 43 65

DATA SET 305

B1 B2

A1 63 61 50 55 58 42 37 43 39 28 24 47 44 43

A2 40 44 57 52 39 35 45 23 22 31 29 31 33 26

A3 62 44 52 42 49 51 47 46 42 31 30 40 41 22

DATA SET 306

B1 B2

A1 70 57 63 62 63 70 61 12 24 12 34 31 24 27

A2 26 50 29 26 26 50 43 35 55 53 44 52 43 49

A3 47 36 57 50 57 54 56 32 42 30 24 41 41 38

DATA SET 307

B1 B2

A1 46 36 54 45 39 59 38 42 39 47 47 37 20 24

A2 49 49 37 49 35 45 62 48 41 40 35 41 36 20

A3 63 55 69 63 79 59 58 40 42 40 41 62 53 64

DATA SET 308

B1 B2

A1 55 58 33 40 47 43 45 18 22 36 33 31 22 12

A2 35 32 23 19 38 25 24 38 41 49 51 53 48 35

A3 44 20 31 38 24 27 28 42 49 42 39 20 37 37

DATA SET 309

B1 B2

A1 54 38 35 41 48 60 62 34 23 24 29 21 45 31

A2 38 44 47 63 59 61 54 44 34 42 31 34 33 29

A3 36 56 42 42 55 36 60 47 22 48 33 43 20 45

DATA SET 310

B1 B2

A1 50 37 47 44 39 39 58 42 45 29 30 32 48 32

A2 40 48 44 39 38 52 44 43 38 42 41 24 29 22

A3 55 42 57 36 47 36 53 37 41 32 29 20 39 30

DATA SET 311

B1 B2

A1 55 42 31 49 54 30 42 22 19 22 28 33 33 28

A2 35 32 35 21 32 37 25 40 50 42 32 30 33 43

A3 49 47 68 54 64 46 64 69 48 59 48 62 47 53

DATA SET 312

B1 B2

A1 43 32 54 33 33 53 30 26 38 34 30 25 19 25

A2 19 36 11 10 35 32 30 34 44 45 50 48 44 58

A3 41 68 59 64 67 52 64 45 62 49 45 48 57 44

DATA SET 313

B1 B2

A1 43 41 45 49 57 36 35 26 35 11 12 32 37 13

A2 15 15 16 23 28 39 38 30 58 47 35 57 47 49

A3 43 69 44 49 44 49 46 56 41 67 53 41 58 45

DATA SET 314

B1 B2

A1 73 56 47 59 56 63 63 14 27 36 33 12 14 18

A2 47 43 27 32 50 39 42 55 46 58 31 43 38 59

A3 58 75 66 66 71 57 57 53 68 52 69 43 65 46

DATA SET 315

B1 B2

A1 56 45 55 46 56 65 54 38 27 11 10 34 37 17

A2 44 49 50 53 44 33 38 47 35 41 33 55 43 37

A3 36 35 57 35 43 46 64 32 38 28 47 48 21 46

DATA SET 316

B1 B2

A1 42 22 41 26 27 38 28 38 47 29 22 37 48 47

A2 37 20 25 38 39 43 41 49 33 32 29 34 38 27

A3 60 48 68 46 52 67 42 55 46 61 55 42 60 58

DATA SET 317

B1 B2

A1 32 38 57 59 46 53 41 36 31 21 27 36 21 38

A2 30 24 13 33 33 10 29 42 40 39 30 43 38 45

A3 27 32 30 29 20 25 32 24 31 45 47 36 39 20

DATA SET 318

B1 B2

A1 36 31 25 21 42 49 36 20 32 21 21 48 24 28

A2 32 48 35 35 29 32 21 27 21 39 23 22 33 22

A3 59 46 42 48 52 67 42 64 59 44 43 55 44 43

DATA SET 319

B1 B2

A1 70 69 61 65 63 69 62 32 18 14 22 25 17 32

A2 42 50 27 46 26 26 31 36 57 41 30 31 44 39

A3 78 61 76 73 73 58 79 69 50 51 56 50 47 59

DATA SET 320

B1 B2

A1 33 42 44 39 55 57 53 15 31 16 12 10 31 39

A2 28 10 11 33 28 36 20 33 44 49 41 45 53 52

A3 59 52 44 42 58 51 58 46 54 61 64 47 67 52

DATA SET 321

B1 B2

A1 59 59 56 70 66 61 51 35 15 26 30 24 37 27

A2 35 42 32 40 33 29 44 51 55 34 35 49 43 38

A3 61 51 47 53 54 44 36 32 39 24 22 28 29 41

DATA SET 322

B1 B2

A1 50 44 53 44 35 31 56 25 26 17 37 33 26 34

A2 32 33 36 21 11 36 16 35 48 49 48 46 42 48

A3 67 46 45 61 61 41 67 55 50 46 52 51 41 42

DATA SET 323

B1 B2

A1 41 48 61 47 55 37 56 25 23 45 45 33 22 21

A2 42 49 35 50 51 61 47 28 38 30 24 36 48 33

A3 44 59 60 47 54 63 49 23 40 41 39 37 46 34

DATA SET 324

B1 B2

A1 57 50 56 52 54 56 30 38 17 13 33 35 24 16

A2 25 13 23 10 31 23 37 44 44 31 33 40 46 39

A3 62 60 69 48 63 66 51 57 40 50 65 60 59 65

DATA SET 325

B1 B2

A1 21 34 23 46 20 37 33 22 43 23 27 32 30 23

A2 48 47 42 31 36 40 48 34 48 41 22 20 22 28

A3 65 54 54 48 69 46 64 43 54 68 42 47 64 57

DATA SET 326

B1 B2

A1 54 36 47 57 42 42 51 17 14 14 12 24 11 25

A2 31 16 10 11 14 30 32 51 33 30 34 31 30 42

A3 53 67 41 49 59 43 63 67 62 52 47 59 41 61

DATA SET 327

B1 B2

A1 45 34 52 55 57 33 46 31 38 38 27 15 14 20

A2 24 23 36 20 34 12 35 55 45 44 44 41 46 36

A3 63 65 42 59 54 69 48 41 54 50 51 61 49 63

DATA SET 328

B1 B2

A1 36 55 36 62 40 62 48 31 32 24 46 37 43 35

A2 61 37 51 48 56 36 42 39 32 24 39 43 34 38

A3 58 38 37 61 56 62 63 42 38 21 26 49 46 32

DATA SET 329

B1 B2

A1 61 46 63 63 53 56 63 38 20 30 41 31 37 48

A2 55 43 45 37 43 45 35 33 43 27 20 38 20 40

A3 62 70 72 80 78 62 67 41 53 46 61 69 49 41

DATA SET 330

B1 B2

A1 52 38 61 38 54 52 37 21 32 46 39 42 24 32

A2 44 44 50 51 61 38 48 32 25 41 46 32 43 40

A3 42 55 47 56 64 42 54 40 40 42 33 44 40 29

8 0

2 years ago

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Arlecino [84]

8/5 or 1.6 you just need to find the rise over the run

6 0

2 years ago

Expand or factor each of the following expressions to determine which expressions are equivalent.​

Expand or factor each of the following expressions to determine which expressions are equivalent.