Rules: Read and answer the following question correctly. Use the correct solution.

Difference of two squares

100

What is the answer? 4x²-36

Solution:√4x²=2x √36=6

Correct answer=(2x+6)(2x-6)

200

What is the answer? 64h⁶-81h

Solution:√64h⁶ = 8h³  √81h=9

Correct answer=(8h³+9)(8h³-9)

300

What is the answer? 16x² -121x⁴

Solution:√16x²=4x √121x⁴=11x²

Correct answer=(4x+11x²)(4x-11x²)

400

What is the answer? 144h²-9h

Solution:√144h^2v=12hv√9h=3h

Correct answer=(12h+3h)(12h-3h)

500

What is the answer? 10x³-40x

Solution:10x(x²-4x)

             √10x²=x √4x=2x

Correct answer=10x(x+2x)(x-2x)

Factoring by common monomial factor

100

What is the answer? 10b⁴+20b²

Solution: GCF= 10b⁴ 

10b²/10b⁴=1b²  10b²/20b²=2

b²-b⁴=b²  b²-b²=b⁰=1

Correct answer = 10b²(1b²+2)

200

What is the answer? 16x²+32x⁴-64x³

Solution: GCF:16x²

16x²/16x²=1  16x²/32x⁴=2x² 16x²/64x³ = 4x¹

x²-x²=x⁰=1   x²-x⁴=x²  x²- x³=x¹

Correct answer=16x²(1+2x²-4x¹)

300

What is the answer? 8x²+12x³-20x⁵

Solution: GCF:4x²

4x²/8x²=2  4x²/12x³= 3x¹ 4x²/20x⁵ = 5x³

x²-x²= x⁰ - x⁰=1  x²-x³=x¹  x²-x⁵= x³ 

Correct answer = 4x²(2+3x¹-5x³)

400

What is the answer? -120x⁴+80

Solution: GCF: -40

-120x⁴/-40=3x⁴ 80/-40=-2

Correct answer=-40(3x⁴-2)

500

What is the answer? 15x⁴+4x³-x

Solution: GCF: x

15x⁴/x=15x³  4x³/x=4x² x/x= 1

Correct answer=x(15x³+4x²-1)

Sum of cubes

100

What is the answer? x⁶+64

Solution: 3√ x⁶= x²  3√ 64=4

(x²)²=x⁴   (4)²=16  x² ⋅ 4 = 4x² 

Correct answer=(x²+4)(x⁴-4x²+16)

200

What is the answer? 125x³+27

Solution 3√125x³=5x 3√27=3 

(5x)² = 25x  (3)² = 9  5x ⋅ 3 =15x

Correct answer= (5x+3)(25x-15x+9)

300

What is the answer? 216x³+27

Solution: 3√ 216x³=6x 3√27=3

(6x)²=36x  (3)²=9 6x⋅3=18x

Correction answer= (6x+3)(36x-18x+9)

400

What is the answer? 64x³+8

Solution: 3√64x³= 4x 3√8 = 2

(4x)²=16x  (2)²=4 4x⋅2= 8x

Correct answer=(4x+2)(16x-8x+4)

500

What is the answer? 32x³+4

_{Solution: GCF:4} 

32x³/4=8x³  4/4=1

3√8x³=2x  3√1=1

(2x)²=4x  (1)²=1  2x⋅1=2x

Correct answer=4(2x+1)(4x-2x+1)

Difference of cubes

100

What is the answer? 8-x³

Solution: 3√8=2 3√x³=x

(2)²=4 (x)²=x²  2⋅x = 2x

Correct answer=(2-x)(4+2x+x²)

200

What is the answer? 27-x³

Solution: 3√27=3 3√x³=x

(3)²=9 (x)² = x²  3⋅x = 3x

Correct answer=(3-x)(9+3x+x²)

300

What is the answer? a³-64b³

Solution: 3√a³=a 3√64b³=4b

(a)²=a² (4b)² = 12b² a⋅4b= 4ab

Correct answer=(a-4b)(a²+4ab+12b²)

400

What is the answer? 125a³-216b³

Solution: 3√125a³=5a  3√216b³=6b

(5a)²=25a² (6b)²=36b² 5a⋅6b=30ab

Correct answer= (5a-6b)(25a²+30ab+36b²⁾

500

What is the answer? 3x³-81

Solution: GCF:3

3/3x³=x³  81/3=27

3√x³=x  3√27=3

(x)² = x²  (3)²=9  x⋅3=3x

Correct answer=3(x-3)(x²+3x+9)