Factorization Of Algebraic Expression Archives

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 (-1/10) of 100z (-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 (a+b) (c+d) (6-x) (3+y) (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 12y +8z The HCF of 12y and 8z is 4 12y +8z 4(12y/4 + 8z/4) 4(3y + 2z) 4n2 2n The HCF of 4n2 and 2n is 2n 4n2 2n 2n(4n2/2n 2n/2n) 2n (2n-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: 2abx + 7acx (b) 3d2e + 5d2 12ax + 8bx WEEKEND ASSIGNMENT Simplify (-6x) x (-x) _____ a) 6x ( b) 6x2 (c) -6x (d) -6x2 Remove brackets from -3(12a 5) a) 15-36a b) 15a-36 c) 15a + 36 d) 36a 15 Expand (a+3)(a+4) (a) a2+7a+12 (b) a2+12a+7 (c) a2+12a-7 (d) a2+7a-12 Factorize abc + abd (a) ab(c+d) (b) ac(b+d) (c) ad(b+c) (d)abc(c+d) Factorize 5a2 + 2ax (a) a(5a+2x) (b) 5(2a2+2x) (c) a(5x+2ax) (d)a2(5+2x) THEORY Expand the following: (p+2q)(p+3q) (5r+2s)(3r+4s) Factorize the following -18fg 12g -5xy + 10y See also DIRECTED NUMBERS APPROXIMATION OF NUMBERS ROUNDING SIMPLE INTEREST FRACTIONS H.C.F & L.C.M AND PERFECT SQUARES