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# Algebra

### Apply algebraic methods in solving problems.

Question | Answer | Skill |
---|---|---|

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: 4ad-8a | =4a(d-2) | Factorising |

Factorise: 2ac+2bc+3ad+3bd | =2c(a+b)+3d(a+b) =(2c+3d)(a+b) | Factorising |

Factorise: x^2+7x+6 | =(x+1)(x+6) | Factorising Quadratics |

Factorise: x^2+x-12 | =(x-3)(x+4) | Factorising Quadratics |

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 |