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 Mathematics Magazine for Grades 1-12  

7/2003

"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)

 

  1. Prove that:

Solution:

 

  1. Prove that:

Solution:







Proposed Exercises: 

Calculate Partial Fractions:

Factor the following expressions:

  1. y2- 6y 55
  2. y3 125