Skip to content

ALGEBRAIC EXPRESSION

    ALGEBRAIC EXPRESSION

    Definition with examples

    Expansion of algebraic expression

    Factorization of simple algebraic expressions

     

    Definition with examples  

    In algebra, letters stand for numbers. The numbers can be whole or fractional, positive or negative.

    Example

    Simplify the following

    • -5 x 2y
    • -3a x -6b
    • -14a/7
    • -1/3 of 36x2

     

    Solution

    1)    -5 x 2y = -5 x (+2) x y

    = -(5 x 2) x y = -10y

    2)    -3a x -6b = (-3) x a (-6) x b

    = (-3) x (-6) x a x b = 18ab

    • -14a/7 = (-14) x a = (-14/7) x a

                                   +7

                = -2 x a = -2a

    4)    -1/3 of 36x2 = (+36) x x2 = – (36/3) x x2

                                            (-3)

    = -12x2

    Evaluation

    Simplify the following

    1.-16x/8

    1. (-1/10) of 100z
    2. (-2x) x (-9y)

     

    Removing brackets

    Example

    Remove brackets from the following

    a.8 (2c + 3d)    (b) 4y (3x-5)   (c) (7a-2b) 3a

    Solution

    8(2c+3d) = 8 x 2c + 8 x 3d

    = 16c + 24d

    b.4y(3x-5) = 4y x 3x – 4y x 5

    = 12xy – 20y

    c.(7a-2b)3a = 7a x 3a – 2b x 3a

    =21a2 – 6ab

     

    Evaluation

    Remove brackets from the following

    1.-5x(11x – 2y)

    2.-p(p – 5q)

    3.(2c + 8d)(-2)

     

    Expanding algebraic expressions

    The expression (a+b)(b-5) means (a+2) x (b-5)

    The terms in the first bracket, (a+2), multiply each term in the second bracket, b-5.

     

    Example

    Expand the following

      1. (a+b) (c+d)
      2. (6-x) (3+y)
      3. (2p-3q) (5p-4)

    Solution

    a.(a+b)(c+d) = c(a+b) + d(a+b)

    = ac+bc+ad+bd

    b.(6-x)(3+y) = 3(6-x) + y (6-x)

    = 18 -3x +6y – xy

    c.(2p-3q)(5p-4) = 5p(2p – 3q)-4(2p-3q)

                              = 10p2 – 15pq – 8p + 12q 

     

    Evaluation

    Expand the following

    • (3+d)(2+d) (b) (3x+4)(x-2)        (c) (2h-k)(3h+2k)         (d) (7m-5n)(5m+3n)

     

    Factorization of algebraic expression

    Example:

    Factorize the following

    • 12y + 8z (b)  4n2 – 2n   (c) 24pq – 16p2

     

    Solution

    1. 12y +8z

    The HCF of 12y and 8z is 4

    12y +8z = 4(12y/4 + 8z/4)

    = 4(3y + 2z)

    1. 4n2 – 2n

    The HCF of 4n2 and 2n is 2n

    4n2 – 2n = 2n(4n2/2n – 2n/2n)

    = 2n (2n-1)

    1. 24pq – 16p2

    The HCF of 24pq and 16p2 is 8p

    24pq – 16p2 = 8p(24pq/8p – 16p2/8p)

    = 8p(3q – 2p)

     

    Evaluation

    Factorize the following:

    1. 2abx + 7acx (b) 3d2e + 5d2
    2. 12ax + 8bx

     

    WEEKEND ASSIGNMENT

    1. Simplify (-6x) x (-x) =_____ a) 6x ( b) 6x2 (c) -6x (d) -6x2
    2. Remove brackets from -3(12a – 5) a) 15-36a b) 15a-36 c) 15a + 36 d) 36a – 15
    3. Expand (a+3)(a+4) (a) a2+7a+12 (b) a2+12a+7 (c) a2+12a-7 (d) a2+7a-12
    4. Factorize abc + abd (a) ab(c+d) (b) ac(b+d) (c) ad(b+c) (d)abc(c+d)
    5. Factorize 5a2 + 2ax (a) a(5a+2x) (b) 5(2a2+2x) (c) a(5x+2ax) (d)a2(5+2x)

     

    THEORY

    Expand the following:

    1. (p+2q)(p+3q)
    2. (5r+2s)(3r+4s)

     

    Factorize the following

    1. -18fg – 12g
    2. -5xy + 10y

     

    See also

    DIRECTED NUMBERS

    APPROXIMATION OF NUMBERS ROUNDING

    SIMPLE INTEREST

    FRACTIONS

    H.C.F & L.C.M AND PERFECT SQUARES

    Leave a Reply

    Your email address will not be published. Required fields are marked *

    Get Fully Funded Scholarships

    Free Visa, Free Scholarship Abroad

               Click Here to Apply

    Index