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# Algebra

### Apply algebraic methods in solving problems.

Expand: 6(x+y) =6×x+6×y =6x+6y Expanding
Expand: -3x(2x-5) =-3x×2x- -3x×5 =-6x^2+15x Expanding
Expand and simplify: (2x+1)(3x-4) =6x^2-8x+3x-4 =6x^2-5x-4 Expanding Two Brackets
Expand and simplify: (3x-2)^2 =(3x-2)(3x-2) =9x^2-6x-6x+4 =9x^2-12x+4 Perfect Squares
Expand and simplify: (2x-5)(2x+5) =4x^2+10x-10x-25 =4x^2-25 Difference of Two Squares
Expand and simplify: (x-2)^3 =(x-2)(x-2)(x-2) =(x^2-4x+4)(x-2) =x^3-2x^2-4x^2+8x+4x-8 =x^3-6x^2+12x-8 More Than Two Brackets
Factorise: 20b-10 =10(2b-1) Factorising
Factorise: 2x^2+12x+16 =2(x^2+6x+8) =2(x+2)(x+4) Two Stage Factorising
Factorise: 3x^2-10x-8 =3x^2+2x-12x-8 =x(3x+2)-4(3x+2) =(x-4)(3x+2) Two Stage Factorising
Simplify: x^2+7x+12 / x+3 =(x+3)(x+4) / x+3 =(x+4) Rational Expressions
Simplify: 2a^2×3a×5a^4 =2×3×5a^(2+1+4) =30a^7 Power Rules
Simplify: 12x^5/6x^4 =12/6x^(5-4) =2x Power Rules
Simplify: (4b^2c^5) =4^2b^(2×2)c^(5×2) =16b^4c^10 Power Rules
Evaluate: (0.5)^-2 =[1/2]^-2 = [2/1]^2 =4 Negative Powers
Write [2/5]^-2 with a positive index and then evaluate. =[5/2]^2 =[25/4] Negative Powers
Simplify and write with a positive index: (xy^2)^-4 =x^(1×-4)y^(2×-4) =x^-4y^-8 =1/x^4y^8 Negative Power Laws
Simplify: (64x^6)^1/2 =√64x^(6×1/2) =8x^3 Negative Power Laws
Evaluate: 64^(2/3) =3*√64^2 =3*√2096 =16 Combining Powers & Roots
Evaluate: 625^(-1/4) =1/(625^1/4) =1/4*√625 =1/5 Fractional & Negative Powers
Simplify: 12x^2y^3z / 27xz^2 =4xy^3/9z Algebraic Fractions
Simplify: 5x^2y/4x × 6y^2/5x^3y =30x^2y^3/20x^4y =3y^2/2x^2 Multiplying Fractions
Simplify: 6r/5 / 3r^2 =6r/5×1/3r^2 =6r×1/5×3r^2 =2/5r Dividing Fractions
Simplify: a/2 + 2a/3 =3×a+2x2a/2×3 =3a+4a/6 =7a/6 Adding Fractions
Simplify: 3/a - 2/b =b×3-a2/a×b =3b-2a/ab Subtracting Fractions
Simplify: 3x+2/4x + 2/6x =6x(3x+2)+4x^2/4x×2/4x×6x =18x^2+12x+8x/24x^2 =18x^2+20x/24x^2 =2x(9x+10)/2x×12x =9x+10/12x Adding Fractions
Simplify: 5/x-1 - 2/x+6 =5(x+6)-2(x-1)/(x-1)(x+6) =5x+30-2x+2/x^2+5x-6 =3x+32/x^2+5x-6 Subtracting Fractions
Expand and simplify: 2(4x+y)+8(3x-2y) =2×4x+2×y+8×3x-8×2y =8x+2y+24x-16y =32x-14y Expanding
Created by: rachelhema