group cycloid

SECOND QUARTER’s PERFORMANCE TASK:SPECIAL PRODUCTSICL: Showcase of Solution and Final Answer

Group Name: CYCLOID

Second Quarter Grade 8 Mathematics Performance Task Special Products 2

Krystal Mizona

Dustine Villa

John Torres

Krystal Mizona

Second Quarter Grade 8 Mathematics Performance Task Special Products 3

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Name:SQUARE OF A BINOMIAL● EASY QUESTION:● (4 + b)

SOLUTION:(4)2 + 2(4 + b) + (b)2

ANSWER:16 + 8b + b2

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Name:SQUARE OF A BINOMIAL● AVERAGE QUESTION:● (13y + 32x)

SOLUTION:(13y)2 + 2(13y + 32x) + (32x)2

ANSWER:169y2 + 832yx + 1024x2

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Name:SQUARE OF A BINOMIAL● CHALLENGING QUESTION:(33y3 + 21k2)

SOLUTION:(33y3)2 + 2(33y3 + 21k2) + (21k2)2

ANSWER:1089y6 + 1386y3k2 + 441k4

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Name:Product of Sum and Difference of Two Terms

● EASY QUESTION:● (a - b) (a + b)

SOLUTION:(a)2 (-b)2

ANSWER:a2 - b2

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Name:Product of Sum and Difference of Two Terms

● AVERAGE QUESTION:(2.43 + a) (2.43 - a)

SOLUTION:(2.43)2 (-a)2

ANSWER:5.9049 - a^2

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Name:Product of Sum and Difference of Two Terms

● CHALLENGING QUESTION:(½ y - 8u4) (½ y + 8u4)

SOLUTION:(½ y)2 + (8u4)2

ANSWER:¼ y2 - 64u8

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Name:SQUARE OF A TRINOMIAL● EASY QUESTION:(m + 4 + 9n)

SOLUTION:(m)2 + (4)2 + (9n)2 + 2(m)(4) + 2(m)(9n) + 2(4)(9n)

ANSWER:m2 + 16 + 81n2 + 8m + 18nm + 72n

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Name:SQUARE OF A TRINOMIAL● AVERAGE QUESTION:(4.6 + 5m + 39y)

SOLUTION:(4.6)2 + (5m)2 + (39y)2 + 2(4.6)(5m) + 2(4.6)(39y) + 2(5m)(39y)

ANSWER:21.16 + 25m2 + 1521y2 + 46m + 358.8y + 390my

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Name:SQUARE OF A TRINOMIAL● CHALLENGING QUESTION:(17t4 + 34a + 2.2x3)

SOLUTION:(17t4)2 + (34a)2 + (2.2x3)2 + 2(17t4)(34a) + 2(17t4)(2.2x3) + 2(34a)(2.2x3) ANSWER:289t8 + 1156a2 + 4.84x6 + 1156t4a + 74.8t4x3 + 149.6ax3

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Name:PRODUCT OF A BINOMIAL AND A TRINOMIAL

● EASY QUESTION:(8 + m) (64 - 16m + m2)

SOLUTION:(8)3 (m)3

ANSWER:512 + m3

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Name:PRODUCT OF A BINOMIAL AND A TRINOMIAL

● AVERAGE QUESTION:(12s + 5i2) (144s2 - 120si2 + 21i4)

SOLUTION:(12s)3 (5i2)3

ANSWER:1728s3 + 125i6

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Name:PRODUCT OF A BINOMIAL AND A TRINOMIAL

● CHALLENGING QUESTION:(42s2t + 33a4r) (1764s4t - 2772s2ta4r + 1089a8r)

SOLUTION:(42s2t)3 (33a4r)3

ANSWER:74088s6t + 35937a12r

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Name:CUBE OF A BINOMIAL● EASY QUESTION:(4 + b)3

SOLUTION:(4)3 + 3(4)2(b) + 3(4)(b)2 + (b)3

ANSWER:64 + 48b + 12b2 + b3

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Name:CUBE OF A BINOMIAL● AVERAGE QUESTION:(35y + 14b)3

SOLUTION:(35y)3 + 3(35y)2(14b) + 3(35y)(14b)2 + (14b)3

ANSWER:42875y3 + 51450y2b + 20580yb2 + 2744b3

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Name:CUBE OF A BINOMIALCHALLENGING QUESTION:(21y4 + 17r3)

SOLUTION:(21y4)3 + 3(21y4)2(17r3) + 3(21y4)(17r3)2 + (17y3)3

ANSWER:9261y12 + 22491y8r3 + 18207y4r6 + 4913y9

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Dustine Villa

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Name: VILLA, DUSTINESQUARE OF A BINOMIAL○ EASY QUESTION:

Square the Binomial (4+5y4).

SOLUTION:(4)2 + 2(4)(5y4) + (5y4)2

FINAL ANSWER:16 + 40y4 + 25y8

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Name:VILLA, DUSTINESQUARE OF A BINOMIAL○ AVERAGE QUESTION: Square the Binomial (4x - 2.3y2).

SOLUTION: (4x)2 + 2(4x)(-2.3y2) + (-2.3y2)2

FINAL ANSWER: 16x2 - 18.4xy2 + 5.29y4

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Name:VILLA, DUSTINESQUARE OF A BINOMIAL○ CHALLENGING QUESTION: Square the Binomial (1/2c7y9 - 2.1x2n5)

SOLUTION:(1/2c7y9)2 + 2(1/2c7y9)(-2.1x2n5) + (2.1x2n5)2

FINAL ANSWER:0.25c14y18 - 2.1c7y9x2n5 + 4.41x4n10

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Name:VILLA, DUSTINEProduct of Sum and Difference of Two Terms○ EASY QUESTION: (5 - n) (5 + n)

SOLUTION:(5)2 -(n)2

FINAL ANSWER:25 - n2

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Name:VILLA, DUSTINEProduct of Sum and Difference of Two Terms○ AVERAGE QUESTION: (21d + x3y7)(21d - x3y7)

SOLUTION:(21d)2 -(x3y7)2

FINAL ANSWER:441d2 - x6y14

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Name:VILLA, DUSTINEProduct of Sum and Difference of Two Terms○ CHALLENGING QUESTION: [( 8 + a ) - 18] [( 8 +

a ) +18]

SOLUTION: (8)2 + 2(8)(a) + (-a)2 - (18)2

FINAL ANSWER: 64 + 16a + a2 - 324

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Name:VILLA, DUSTINESQUARE OF A TRINOMIAL○ EASY QUESTION: (m2 + 3n + 2)2

SOLUTION: (m2)2 + (3n)2 + (2)2 + 2(m2)(3n) + 2(m2)(2) + 2(3n)(2)

FINAL ANSWER:m4 + 3n4 + 4 + 6m2n + 4m2 + 12n

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Name:VILLA, DUSTINESQUARE OF A TRINOMIAL○ AVERAGE QUESTION: (0.3x4 + 2.1m3 - 1.2d5)2

SOLUTION:(0.3x4)2 + ( 2.1m3)2 + (-1.2d5)2 + 2(0.3x4)(2.1m3) + 2(0.3x4) (-1.2d5) + 2( 2.1m3)(-1.2d5)

FINAL ANSWER: 0.09x8 + 4.41m6 + 1.44d10 + 1.26x4m3 - 0.72x4d5 - 5.04m3d5

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Name:VILLA, DUSTINESQUARE OF A TRINOMIAL○ CHALLENGING QUESTION:Find the area of a square lot whose side measures (6d +7c2 - 21n) meters.

SOLUTION: S2 = (6d +7c2 - 21n) 2

(6d)2 + (7c2)2 + (-21n)2 + 2(6d)(7c2) + 2(6d)(-21n) + 2(7c2)(-21n)

FINAL ANSWER: 36d2 + 49c4 + 441n2 + 84dc2 - 252dn - 294c2n

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Name:VILLA, DUSTINEPRODUCT OF A BINOMIAL AND A TRINOMIAL○ EASY QUESTION: (2 + 4x) (4 - 8x +16x)

SOLUTION:(2)3 + (4x)3

FINAL ANSWER:8 + 64x3

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Name:VILLA, DUSTINEPRODUCT OF A BINOMIAL AND A TRINOMIAL○ AVERAGE QUESTION: (12r6d - 2m8b) (144r12d +

24r6dm8b+ 4m8b)

SOLUTION:(12r6d)3 + (-2m8b)3

FINAL ANSWER1,728r18d + 8m24b

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Name:VILLA, DUSTINEPRODUCT OF A BINOMIAL AND A TRINOMIAL○ CHALLENGING QUESTION: Find the area of a rectangular lot whose length and width measures (0.5d + 3.4m4n2)(0.25d2 - 1.7dm4n2 + 11.56m8n4)

SOLUTION:(0.5d)3 + (3.4m4n2)3

FINAL ANSWER:0.125d + 39.204m12n6 square meters.

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Name:VILLA, DUSTINECUBE OF A BINOMIAL○ EASY QUESTION: (a + b5)3

SOLUTION: (a)3 + 3(a)2(b5) + 3(a)(b5)2 + (b5)3

FINAL ANSWER:a3 + 3a2b5 + 3ab10 + b15

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Name:VILLA, DUSTINECUBE OF A BINOMIAL○ AVERAGE QUESTION: (1.8g8 - 5v4)3

SOLUTION:(1.8g8)3 + 3(1.8g8)2(- 5v4) + 3(1.8g8)(- 5v4)2 + (- 5v4)3

FINAL ANSWER:5.832g24 - 32.4g16v4 + 135g8v8 - 125v12

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Name:VILLA, DUSTINECUBE OF A BINOMIAL○ CHALLENGING QUESTION: Find the volume of a cube whose edge measure ( 5v3 + 10x5) meters.

SOLUTION:( 5v3)3 + 3( 5v3)2 (10x5) + 3( 5v3)(10x5)2 + (10x5)3

FINAL ANSWER:125v9 + 750v6x5 + 1,500v3x10 + 1,000x15 cubic meters.

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CARLO TORRES

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∗EASY QUESTION:

( H+B )^2

SOLUTION:( H )^2+2( H ) ( B )+( G )^2

ANSWER:H^2+2HB+G^2

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∗AVERAGE QUESTION:

(c^3b-d^2)2

SOLUTION:(c^3b)2+2(c^3b)(d^2)+(d^2)2

ANSWER:c^6b+c^6bc^4+c4

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∗CHALLENGING QUESTION:

(½+10y^5)^2

SOLUTION:(½)^2+2(½)(10y^5)+(10y^5)^2

ANSWER:¼+10y^5+100y^10

Name:SQUARE OF A BINOMIAL

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∗EASY QUESTION:

(c+a)(a-c)

SOLUTION:( c )^2 ( a )^2

ANSWER:c^2-a^2

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∗AVERAGE QUESTION:

(a^2 + b^3)(a^2 + b^3)

SOLUTION:(a^2)^2 (b^3)^2

ANSWER:a^4 - b^6

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∗CHALLENGING QUESTION:

[(a+b) - 12][(a+b) - 12]

SOLUTION:[(a+b) - 12] [(a+b)+12]ANSWER:a^2+2ab+n^2 - 144

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∗EASY QUESTION:

(x+4y+4)^2

SOLUTION:(X)^2+(4y)^2+(4)^2+2(x)(4y)+2(x)(4) + 2(4y)(4)

ANSWER:x^2+16y^2+16+8xy+ 8x +16y

Name:SQUARE OF A TRINOMIAL

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∗AVERAGE QUESTION:

4a^2+12ab+9b^2

SOLUTION:(4a^2)^2+(12ab)^2+(9b^2)^2+2(4a^2)(12ab)+2(4a^2)(9b^2)+2(12ab)(9b^2)

ANSWER:16a^4+144ab^2+81b^4+96ab^4+72b^8+216ab^4

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∗CHALLENGING QUESTION:(9/3a^3-4x^4+12)^2

SOLUTION:(9/3a^3)^2 + (-4b^4)^2 + (12)^2 + 2(9/3a^3)(-4b^4) + 2(9/3a^3)(12) + 2(-4b^4)(12)ANSWER:9a^6 + 16b^8 + 144 - 24a^4b^3 + 72a^3 - 96b^4

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∗EASY QUESTION:

(b^2+2) (b^4-4b^2+4)

SOLUTION:(b^2)^3 (2)^3

ANSWER:b^6+ 8

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∗AVERAGE QUESTION:(4a^2-b^3) (16a^4+8a^2b^3+b^6)

SOLUTION:(4a^2)^3 (b^3)^3

ANSWER:64a^6+b^9

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∗CHALLENGING QUESTION:

(2/3g^2+4/5h) (4/9g^4-16/15g^2h+16/25h^2)

SOLUTION:(2/3g^2)^3 ( 4/5h)^3

ANSWER:8/27g^6+64/125h^3

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∗EASY QUESTION:

(b+a)^3SOLUTION:

(b)^3+3(b)^2(a)+3(b)(a)^2+(a)^3ANSWER:b^3 +3b^2a+3ba^2+a3

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∗AVERAGE QUESTION:

(1.2+4.6)^3

SOLUTION:(1.2)^3+3(1.2)^2 (4.6)+3(1.2) (4.6)^2+(4.6)^3

ANSWER:1.728+16.56+76.176+97.336

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∗CHALLENGING QUESTION:

(2/5b^3+⅗)^2

SOLUTION:(2/5b^3)^3+3(2/5b^3)^2 (⅗)+3(2/5b^3) (⅗)^2+(⅗)^3

ANSWER:8/125+9/25b^6+18/25b^3+27/125

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RECLECTIONGroup Name _CYCLOID_

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Krystal Mizona

In this Peta it helped me in creating my own problem to solve. This peta also helped our environment in saving trees because this peta is paperless. It helped me to understand more about solving all the problems in math algebra. It’s not easy for me to create a problem.

Second Quarter Grade 8 Mathematics Performance Task Special Products 52

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Dustine VillaI LEARNED HOW TO TO HELP WITHOUT CAUSING BAD EFFECTS TO THE SOCIETY THROUGH THIS PAPERLESS PETA. I ALSO LEARNED TO APPRECIATE OUR TEACHERS WHO GIVE TIME TO MAKE POWERPOINTS FOR US TO UNDERSTAND THE LESSONS THAT WOULD REALLY BE HOPEFUL FOR US IN THE FUTURE. I HAVE ALSO UNDERSTAND THE EFFECT THIS PETA WOULD MAKE TO EVERYONE , SPECIALLY TO THE STUDENTS LIKE ME. I HAVE FULLY UNDERSTAND AND PRACTICED THE LESSONS (SPECIAL PRODUCTS) THROUGH THIS PETA/ICL 1. I THANK GOD AND SIR CAPARAS FOR THIS OPPORTUNITY TO HELP AND PRACTICE SPECIAL PRODUCTS AND I LOOK FORWARD TO MORE PETAS LIKE THIS.Second Quarter Grade 8 Mathematics Performance Task Special Products 53

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John Torres

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I have learned many things.Like solving my own problem,Like solving for square of trinomial and also cube of binomial.And also i know the steps of how to solve algebra in easy way.