Tuesday, February 24, 2009

Expansion

From factorisation you can get back the original by expansion

Recall what is a term. A term is separated by + or - or =
A term consists of parts.
A book is on ething and consist of parts, toc, chapters, cover, pages, etc
Similarily, a term consists of parts, eg

2 + 3mn + 6twb -12 def + 1/2 mb = 120

This equation consists of 6 terms
  • 2 is a number term and is a 1 part
  • 3mn is a mn term and consists of 3 parts, a number, a m and a n
  • 6twb is a twb term and consists of 4 terms, a number, a t, a w and a b
  • 12def is a def term and consists of 4 parts, a number, a d, a e and a f
  • 1/2 mb is a mb term and consists of 3 parts, anumber, a m and a b
  • 120 is a number and is a 1 part

Identify how many terms are present in the equation, what are the trem, and what are the parts.

  1. 12 mn + 3mds
  2. 2m^2 + m
  3. 6mn - 3mpd + 2 m^2
  4. 20 m^2 - m
  5. 6mnt - 3mn

For each of the above look for any common part in all the term.

This will go outside the bracket ( ) and inside the bracket put what reamins in each term

26 comments:

  1. 12 mn is a mn term and consist of three parts, a number, a m and a n

    3 mds is a mds term and consists of four parts a number a m , a d and a s.

    ReplyDelete
  2. 6mnt - 3mn

    6mnt is a term and consists of four parts a number , a m , a n and a t.

    3mn is a term and consists of three parts a number a m and a n.

    ReplyDelete
  3. 12 mn + 3mds
    common term is m

    3m ( 4n + ds)

    ReplyDelete
  4. 6mnt - 3mn

    the common terms are m and n
    mn ( 6t - 3)

    ReplyDelete
  5. 2m^2 + m

    m is the common term

    m ( 2 m + 1)

    ReplyDelete
  6. 12mn is the term in this case
    12mn consist of three parts; number,m,and n

    3mds is the term in this case
    3mds cosists of four parts;number,m,d and s

    ReplyDelete
  7. 2) 2m^2+m
    m is common in the first term and 2nd term
    Pull out m
    Therefore m(2m+1)

    ReplyDelete
  8. 3)6mn-3mpd+2m^2
    I first rearrange the equation
    2m^2+6mn-3mpd
    m is common in all the terms so i pull it
    out of the brackets.
    therefore i get; m(2m+6n-3pd)

    ReplyDelete
  9. 20m^2-m
    m is common in this case
    therefore m(20^2-1)
    note that m divided in m=1
    m is in the first and second term
    it was pulled out

    ReplyDelete
  10. 5) 6mnt-3mn
    mn are the common terms
    3 is a factor of 6
    therefore 3mn will be pulled out
    3mn(2t-1)

    6mnt consist of four parts;a number,m,n,t
    -3mn consist of 3 parts;a number,m,n.

    ReplyDelete
  11. 12 mn + 3mds
    the commonn term is 3m since m is common in both terms and 3 is a factor of 12.
    ans.= 3m(4n + ds)

    ReplyDelete
  12. 2m^2 + m
    the common trem is m.
    ans.= m(2m + 1)

    ReplyDelete
  13. 6mn - 3mpd + 2 m^2
    the common term is m.
    ans.= m(6n -3pd + 2m)

    ReplyDelete
  14. 20 m^2 - m
    the common term is m.
    ans.= m(20m - 1)

    ReplyDelete
  15. 6mnt - 3mn
    the common term is 3mn.
    ans.=3mn(2t - 1)

    ReplyDelete
  16. 1)12 mn + 3mds
    12mn is a mn term and consist of three parts, number, m and n

    3mds is a mds term and consists of four parts number, m, d, and s.

    3m is a factor of both terms and therefore will be placed outside the bracket.
    sol: 3m ( 4n + ds)

    ReplyDelete
  17. 2)2m^2 + m
    2m^2 is a m^2 term and consists of two parts number, m^2

    m is a m term consisting of one part, m.

    m is a factor of both terms and therefore will be placed outside the

    bracket.
    sol: m(2m + 1)

    ReplyDelete
  18. 3)6mn - 3mpd + 2 m^2
    6mn is a mn term consting of 3parts number, m, n.

    3mpd is a mpd term consisting of four parts number, m, p, d.

    2 m^2 is a m^2 term consisting of 2parts, number, m^2

    m is a factor of three terms and therefore will be placed outside the

    bracket.
    sol: m(6n -3pd + 2m)

    ReplyDelete
  19. 4)2m^2 - m
    2m^2 is a m^2 term and consists of two parts number, m^2

    m is a m term consisting of one part, m.

    m is a factor of both terms and therefore will be placed outside the

    bracket.
    sol: m(2m - 1)

    ReplyDelete
  20. 5)6mnt - 3mn
    6mnt is a mnt term consisting of four parts number, m,n,t

    3mn is a mn term consisting of three parts number m,n

    3mn is a factor of three terms and therefore will be placed outside the

    bracket.
    sol: 3mn(2t - 1)

    ReplyDelete
  21. My question and answer!!

    What is the expansion of (x+2)^4

    ReplyDelete
  22. ANSWER
    This problem is straightforward if you take it step by step.

    First, (x + 2)^4 = (x + 2) (x + 2) (x + 2) (x + 2)

    Step 1 is to begin with (x + 2) (x + 2). To do this, you multiply each of the elements from the first parenthesis times each of the items in the second. So, you get:

    x * x = x^2

    x * 2 = 2x

    2 * x = 2x

    2 * 2 = 4

    Add these together, and you get x^2 + 4x + 4

    Step 2 is to multiply all that first by x:

    x^3 + 4x^2 + 4x

    and then by 2:

    2x^2 + 8x + 8.

    Add them all together and you get: x^3 + 6 x^2 + 12x + 8.

    Step 3 is to multiply all that by the last (x + 2).

    First by x: x^4 + 6x^3 + 12x^2 + 8x

    then by 2: 2x^3 + 12 x^2 + 24x +16

    Add those two together and simplify for the final answer:

    x^4 + 8x^3 + 24x^2 + 32x +16

    ReplyDelete
  23. 6mn - 3mpd + 2 m^2

    6mn is a mn term and consists of three parts a number 6 a m and a n.

    3mpd is a mpd term and consists of a number 3 a m, a p and a d

    2mn^2

    2 m n ^2 is a mn^2 term and consists of a m and a n^2

    ReplyDelete
  24. 12mn+3mds
    well in the first part of the question 12mn there are three parts.......
    these are a number, m and n

    in the second part 3mds it consist of four parts these are a number,m , d and s

    therefore when expanded= 3m(4n+ds)

    ReplyDelete
  25. 2. 2m^2 + m
    in the first part of the equation 2m^2
    it consist of two parts a number and m

    in the second they is only one part which is m
    *note ...when solving an equation you should extract like terms

    eqn'2m^2+m
    solution.... m(2m+1)

    ReplyDelete
  26. 3. 6mn - 3mpd + 2 m^2
    6mn consist of three parts a number,
    m and n.
    3mpd consist of four parts a number,
    m, p, and d.
    2m^2 consist of two parts a number and m^2

    when this equation is worked
    you first extact the like terms which is "m" this helps you to get your solution easily...

    sol.. 6mn - 3mpd + 2 m^2
    = m(6n-3pd+2m)

    ReplyDelete