chapter 1 and 2

  • natural numbers: positive counting #s w/out 0

  • whole numbers are natural w/ 0

  • intergers : whole numbers w/ negative number

  • rational numbers: numbers expressed as fractions, ratios, or denominator doesn’t = 0

  • irrational numbers: 3.33333333333333333333

  • real numbers: pretty much everything

  • Commutative: a x b= b x a

  • Association: a(b + c)= b(c+a)

  • When there is negative exponent then send to the bottom

1.2

  • Multiplication adds exponents

  • To a power multiply

aman=am−n\frac{a^{m}}{a^{n}}=a^{m-n}

  • (3a)−2\left(3a\right)^{-2} : don’t forget 3a x 3a = 9a²

1.3

ab=ab\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}

933⋅3⋅3=939=3\frac{9}{3\sqrt3}\frac{\cdot\sqrt3}{\cdot\sqrt3}=\frac{9\sqrt3}{9}=\sqrt3 cause 9 cancels out

  • 5\sqrt{15}+5\sqrt{135}->5\sqrt9\cdot\sqrt{15} get to the same radical

  • 42+3⋅(2−3)⋅(2−3)\frac{4}{2+\sqrt3}\frac{\cdot\left(2-\sqrt3\right)}{\cdot\left(2-\sqrt3\right)} if the denominator is not ab\sqrt{b}

  • x32=x⋅x12=xxx^{\frac32}=x\cdot x^{\frac12}=x\sqrt{x}

1.5

  • a3+b3a^3+b^3 = (a+b)(a2−ab+b2)\left(a^2-ab+b^2\right)

2.3

y1−y2x1−x2\frac{y^1-y^2}{x^1-x^2}

2.4

y−y1=m(x−x1)y-y^1=m\left(x-x^1\right)

2.5

x2+x=3x^2+x=3

Half of b term(1) then square it add to both sides

x2+x+14=3+14x^2+x+\frac14=3+\frac14

Group left side

(x+12)2=134\left(x+\frac12\right)^2=\frac{13}{4}

Solve from their

  • Discrimination formula: b2−4acb^2-4ac

  • Less than 0 two imagine

  • Equal 0 1 real solution

  • More than 0 2 real solution

2.7

  • Do the inequalities the easy way