Algebraic Identities

Using (a+b)^2

100

Expand (x + 5)²

x²+ 10x + 25

200

Expand (2x+y)²

4x² + y² + 4xy

300

Free points!!!!

Good for you!

400

Calculate quickly: (101)²

(100+1)²=100²+2.100.1+1²=10000+200+1=10201

500

Expand (2x⁴ + y³)²

4x⁸ + 4x⁴y³ + y⁶

Using (a+b)(a-b)

100

Expand: (x+2)(x-2)

x^2 - 4

200

Expand: (xy - ab)(xy + ab)

x²y²- a²b²

300

Swap points

Yayyy

400

Compute: 101²-99²

(101-99)(101+99)

500

Expand: (x²y² - 1)(x²y² + 1)

x⁴y⁴ - 1

Using (a-b)^2

100

Expand: (3x - 1)²

9x² -6x+1

200

Expand: (2x - 10y)²

4x² - 40xy + 100y²

300

Expand: (8x² - 5y²)²

64x⁴ + 25y⁴ - 80x²y²

400

400 points for free

!!!

500

Compute: 99²

(100-1)²=100²-2.100.1+1²=10000-200+1=9801

Mixed Identities

100

Expand (a²+b²)²

a⁴+ 2a²b²+ b⁴

200

Expand (5y+3)(5y - 3)

25y² - 9

300

No point here!

Oh no!

400

Expand: (xy³ + 4)(xy³ - 4)

x²y⁶ - 16

500

Expand: (5a⁴ - 9b⁴)²

25a⁸ - 90a⁴b⁴ + 81b⁸

minimum/maximumvalue

100

Find the minimum value of (x-1)²+8

8

200

What is the minimum value of x²+2x+1

0

300

Free points

!!

400

What is the maximum value of -x²+4x+16

20

500

What is the minimum value of x² − 2xy + 2y² − 4y + 10

6