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Use Pascal's triangle to expand the binomial. 1) (s + t)^3

Question : Use Pascal's triangle to expand the binomial. 1) (s + t)^3 : 2151531

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use Pascal's triangle to expand the binomial.

1) (s + t)3

A) s3 + s2t + st2 + t3

B) s3 + t3

C) s3 + 3s2t + 3st2 + t3

D) s3 + 4s2t + 6st + 4st2 + t3

2) (a + b)4

A) a4 + 5a3b + 10a2b2 + 10ab + 5ab3 + b4

B) a4 + b4

C) a4 + 4a3b + 6a2b2 + 4ab3 + b4

D) a4 + a3b + a2b2 + ab3 + b4

3) (p + q)5

A) p5 + 6p4q + 15p3q2 + 20p3q3 + 15p2q3 + 6pq4 + q5

B) p5 + p4q + p3q2 + p2q3 + pq4 + q5

C) p5 + q5

D) p5 + 5p4q + 10p3q2 + 10p2q3 + 5pq4 + q5

4) (c + d)6

A) c6 + 7c5d + 21c4d2 + 35c3d3 + 35cd + 21c2d4 + 7cd5 + d6

B) c6 + 6c5d + 15c4d2 + 20c3d3 + 15c2d4 + 6cd5 + d6

C) c6 + c5d + c4d2 + c3d3 + c2d4 + cd5 + d6

D) c6 + d6

5) (m - n)5

A) m5 - 5m4n - 10m3n2 - 10m2n3 - 5mn4 - n5

B) m5 - n5

C) m5 - 6m4n + 15m3n2 - 20m3n3 + 15m2n3 - 6mn4 + n5

D) m5 - 5m4n + 10m3n2 - 10m2n3 + 5mn4 - n5

6) (x - y)6

A) x6 - x5y + x4y2 - x3y3 + x2y4 - xy5 + y6

B) x6 - y6

C) x6 - 6x5y - 15x4y2 - 20x3y3 - 15x2y4 - 6xy5- y6

D) x6 - 6x5y + 15x4y2 - 20x3y3 + 15x2y4 - 6xy5 + y6

Evaluate the expression.

7) (5!/3!)

A) 5

B) 20

C) 2!

D) (5/3)

8) (4!/6!)

A) 30

B) (1/30)

C) (1/2!)

D) 2!

9) (5!/3! 2!)

A) 1

B) 5

C) 10

D) 0!

10) (4!/3!)

A) 1

B) 4

C) (4/3)

D) 4!

11) (10!/5!5!)

A) 30,240

B) 252

C) 126

D) 504

12) (4!/2! 2!)

A) 12

B) 6

C) 1

D) 4

13) (7!/3! 4!)

A) 35

B) 1

C) 210

D) 7

14) (6!/0!)

A) 360

B) undefined

C) 120

D) 720

Use the binomial formula to expand the binomial.

15) (w - s)6

A) w6 - 6w5s + 15w4s2 - 20w3s3 + 15w2s4 - 6ws5 + s6

B) w6 - 8w5s + 17w4s2 - 22w3s3 + 17w2s4 - 8ws5 + s6

C) w6 - s6

D) w6 - 6w5s - 30w4s2 + 120w3s3 + 360w2s4 - 720ws5 - 720s6

16) (g - 2h)3

A) g3 - 8g2h + 12gh2 - 6h3

B) g3 - 6g2h + 12gh2 - 8h3

C) g3+6g2h - 12gh2 + 8h3

D) g3 - 6gh + 12gh2 - 8h3

17) (x - 1)6

A) x6 - 6x5 - 15x4 - 20x3 - 15x2 - 6x - 6

B) x6 - 6x5 +30x4 - 120x3 + 30x2 - 6x + 1

C) x6 - 6x5 +15x4 - 20x3 + 15x2 - 6x + 1

D) x6 - 6x5 - 30x4 - 120x3 - 360x2 - 720x + 720

18) (x + 3)5

A) x5 + 15x4 + 90x3 + 270x2 + 405x + 243

B) x5 + 15x4 + 90x3 + 270x2 + 405x + 3

C) x5 + 15x4 + 180x3 + 540x2 + 405x + 3

D) x5 + 15x4 + 180x3 + 540x2 + 405x + 243

19) (5x + 4)3

A) 125x3 + 300x2 + 240x + 64

B) 125x3 + 300x2 + 300x + 64

C) 25x2 + 40x + 16

D) 25x6 + 20x3 + 4096

20) (4x - 2)4

A) 256x4 - 512x3 + 384x2 - 128x + 16

B) 256x3 - 512x2 + 384x - 128

C) -512x4 + 1024 x3 + 384x2 + 256x + 16

D) (16x2 - 8x + 4)4

21) (4x - 2)5

A) 1024x5 + 320x4 - 1280x3 - 1280x2 + 320x - 32

B) 1024x5 - 2560x4 + 2560x3 - 1280x2 + 320x - 32

C) 1024x5 - 512x4 + 256x3 - 128x2 + 64x - 32

D) (16x2 - 16x + 4)5

22) (4x2 + 1)3

A) (16x4 + 8x2 + 1)3

B) 256x8 + 64x6 + 48x4 + 12x2 + 1

C) 64x6 + 48x4 + 12x2 + 1

D) 64x3 + 48x2 + 12x + 1

23) (4x - 5y)3

A) 64x3 - 80x2y + 100xy2 - 125y3

B) 16x3y - 20x2y2 + 25xy3

C) 16x3y - 40x2y2 + 25xy3

D) 64x3 - 240x2y + 300xy2 - 125y3

24) (2x + y)6

A) 64x6 + 192x5y + 240x4y2 + 160x3y3 + 240x2y4 + 192xy5 + 64y6

B) 2x6 + 12x5y + 30x4 y2 + 40x3y3 + 12xy5 + y6

C) 64x6 + 192x5y + 480x4y2 + 960x3y3 + 1440x2y4 + 12xy5 + y6

D) 64x6 + 192x5y + 240x4 y2 + 160x3 y3 + 60x2y4 + 12xy5 + y6

Find the indicated term.

25) The fourth term of the expansion of (s - t)12

A) 495s8t4

B) - 220s9t3

C) - s9t3

D) s8t4

26) The third term of the expansion of (3x + 5)3

A) 135x2

B) 450x

C) 225x

D) 25

27) The third term of the expansion of (5x + 2)3

A) 120x

B) 150x2

C) 24

D) 60x

28) The ninth term of the expansion of (4x + y)8

A) 4y8

B) y8

C) 32xy7

D) y9

29) The third term of the expansion of (2x + 3)3

A) 54x

B) 36x2

C) 108x

D) 9

30) The fifth term of the expansion of (5x + 4)5

A) 5120

B) 8000x2

C) 6400x

D) 1600x

Provide an appropriate response.

31) Expand the expression (x - (3/√(x)))4.

A) x4 - 12x5/2 + 54 - (108/√(x)) + (81/x2)

B) x4 - 12x3/2 + 54x - (108/√(x)) + (81/x2)

C) x4 - 12x5/2 + 54x - (108/√(x)) + (81/x)

D) x4 - 12x5/2 + 54x - (108/√(x)) + (81/x2)

32) Find the term containing x2 in the expansion of (√(x) + √(3))8.

A) 630x2

B) 70√(3)x2

C) -70√(3)x2

D) -630x2

The notation ((n/r)) means ((n!/r!(n - r)!)). Evaluate the expression.

33) (10 is over 5)

A) 126

B) 2

C) 30,240

D) 252

34) (9 is over 9)

A) 2

B) 1

C) 362,880

D) 0

35) (236 is over 3)

A) 12,977,640

B) 233

C) (236!/233!)

D) 2,162,940

36) (7 is over 0)

A) 0

B) 5040

C) 1

D) 2

Solution
5 (1 Ratings )

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