viel glück

Expansion

100

2(h + k) - (h - k) 

h + 3k

200

(14x + 13y)(14x - 13y)

196x² - 169y²

300

abc(a - b + c)

a²bc - ab²c + abc²

400

(x + 1)³

x³ + 3x² + 3x + 1

500

Selamat :>

(2a - b)(4a² + 2ab + b²) - a³ + b³

7a³

Factorization

100

2b + b² = ??

b(b +2)

200

x² - 5x + 6 = ??

(x - 2)(x - 3)

300

Factorize

3x² + 5xy - 2y²

(x + 2y)(3x - y)

400

2(a-1)² + (a-1) - 3 [Hint: let (a-1) = X]

(a - 2)(2a + 1)

500

Factorize COMPLETELY

x³² - y³²

(x¹⁶+y¹⁶)(x⁸+y⁸)(x⁴+y⁴)(x²+y²)(x + y)(x - y)

Algebraic Rules

100

If p - q =15, evaluate

3p - 3q - 2

43

200

If 

x + y = 8

x² - y² = -16

Find x - y

-2

300

Evaluate 9999²

99,980,001

400

If:

x + y = 8

xy = 2

Find x² + y²

60

500

If x + 1/x = 3

Evaluate x³ + 1/x³

[Hint: a³ + b³ = (a+b)(a² - ab + b²)]

18

Logarithms

100

Solve for x in:

log_x5 = 2

√5

200

Evaluate the following integral

∫e^ln(5x⁴sin(x⁵))dx

jk lol free points [ans was -cos(x⁵) + C]

300

Express as a single logarithm:

log4 - (logP + logQ) + 2logR

log(4R²/PQ)

400

Solve for the values of x:

1 + 2log₃x = log₃(28x - 9)

x = 1/3

x = 9

500

Solve for x in:

(log₃x)² - log₃x^log100 = -log₃3

x = 3

Functions

100

Find the midpoint of A(6,7) and B(4,1)

(5,4)

200

Find the coordinate of the turning point in

y = -x² + 6x - 4

(3,5)

300

Find the value(s) of x where y isn't defined in

y = 5 + 1/(x-2) 

x = 2

400

Find the perpendicular bisector of the points A(3,5) and B(6,7)

y = (-3/2)x + (51/4)

500

The distance of a particle from the origin is given as

D = t³ - 3t² + 2

Where t is time in seconds D is the distance traveled in metres. Evaluate the velocity of the particle three seconds after it starts moving (at t = 3).

[Hint: Velocity is the first derivative of D]

9m/s