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 |