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 36x^{2}
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 36x^{2} = (+36) x x^{2} = – (36/3) x x^{2}
^{ } (3)
= 12x^{2}
Evaluation
Simplify the following
1.16x/8
 (1/10) of 100z
 (2x) x (9y)
Removing brackets
Example
Remove brackets from the following
a.8 (2c + 3d) (b) 4y (3x5) (c) (7a2b) 3a
Solution
8(2c+3d) = 8 x 2c + 8 x 3d
= 16c + 24d
b.4y(3x5) = 4y x 3x 4y x 5
= 12xy 20y
c.(7a2b)3a = 7a x 3a 2b x 3a
=21a^{2} 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)(b5) means (a+2) x (b5)
The terms in the first bracket, (a+2), multiply each term in the second bracket, b5.
Example
Expand the following

 (a+b) (c+d)
 (6x) (3+y)
 (2p3q) (5p4)
Solution
a.(a+b)(c+d) = c(a+b) + d(a+b)
= ac+bc+ad+bd
b.(6x)(3+y) = 3(6x) + y (6x)
= 18 3x +6y xy
c.(2p3q)(5p4) = 5p(2p 3q)4(2p3q)
= 10p^{2} 15pq 8p + 12q
Evaluation
Expand the following
 (3+d)(2+d) (b) (3x+4)(x2) (c) (2hk)(3h+2k) (d) (7m5n)(5m+3n)
Factorization of algebraic expression
Example:
Factorize the following
 12y + 8z (b) 4n^{2 } 2n (c) 24pq 16p^{2}
Solution
 12y +8z
The HCF of 12y and 8z is 4
12y +8z = 4(12y/4 + 8z/4)
= 4(3y + 2z)
 4n^{2} 2n
The HCF of 4n^{2} and 2n is 2n
4n^{2} 2n = 2n(4n^{2}/2n 2n/2n)
= 2n (2n1)
 24pq 16p^{2}
The HCF of 24pq and 16p^{2} is 8p
24pq 16p^{2} = 8p(24pq/8p – 16p^{2}/8p)
= 8p(3q 2p)
Evaluation
Factorize the following:
 2abx + 7acx (b) 3d^{2}e + 5d^{2}
 12ax + 8bx
WEEKEND ASSIGNMENT
 Simplify (6x) x (x) =_____ a) 6x ( b) 6x^{2} (c) 6x (d) 6x^{2}
 Remove brackets from 3(12a 5) a) 1536a b) 15a36 c) 15a + 36 d) 36a 15
 Expand (a+3)(a+4) (a) a^{2}+7a+12 (b) a^{2}+12a+7 (c) a^{2}+12a7 (d) a^{2}+7a12
 Factorize abc + abd (a) ab(c+d) (b) ac(b+d) (c) ad(b+c) (d)abc(c+d)
 Factorize 5a^{2} + 2ax (a) a(5a+2x) (b) 5(2a^{2}+2x) (c) a(5x+2ax) (d)a^{2}(5+2x)
THEORY
Expand the following:
 (p+2q)(p+3q)
 (5r+2s)(3r+4s)
Factorize the following
 18fg 12g
 5xy + 10y
See also
APPROXIMATION OF NUMBERS ROUNDING
H.C.F & L.C.M AND PERFECT SQUARES
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