"Learning is the beginning of wealth. Learning is the beginning of health. Learning is the beginning of spirituality. Searching and learning is where the miracle process all begins." – Jim Rohn

Grade 9

Theory

 Polynomial Identities

(a+b) ² = a ² + 2ab + b ²

(a+b)(c+d) = ac + ad + bc + bd

a ² - b ² = (a+b)(a-b) (Difference of squares)

a ³ b ³ = (a b)(a ² ab + b ²) (Sum and Difference of Cubes)

x ² + (a+b)x + ab = (x + a)(x + b)

If ax ² + bx + c = 0 then x =  (Quadratic Formula)

Solutions from the Previous Issue:

1. Calculate cos(3u) in terms of cos(u)

Solution:

cos(2u+u) =

cos(2u)cos(u)-sin(2u)sin(u) =

cos²(u)-sin²(u))cos(u)-2sin(u)cos(u)sin(u) =

cos³(u) - sin²(u)cos(u)-2sin²(u)cos(u) =

cos³(u) -3sin²(u)cos(u)

cos³(u) -3cos(u)+3cos³(u)

4cos³(u) -3cos(u)

In the same way

sin(3u) = - 4sin³(u) -3sin(u)

2. Prove that:

Solution:

3. Prove that:

Solution:

Proposed Exercises: 

Calculate Partial Fractions:

Factor the following expressions:

2. y²- 6y – 55
3. 
4. y³ – 125