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### 29 Cards in this Set

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 exponents: multiplying powers with the same base (x^m)(x^n)=x^(m+n) exponents: dividing powers with the same base (x^m)/(x^n)=x^(m-n) exponents: raising a power to an exponent (x^m)^n= x^mn exponents: multiplying powers with the same exponent (x^n)(y^n)=(xy)^n exponents: dividing powers with the same exponent (x^n)/(y^n)=(x/y)^n combining like terms 2a+3a=(2+3)a=5a adding or subtracting polynomials combine like terms multiplying monomials multiply coefficients separately 2x*3x=(2*3)(x*x)=6x^2 multiplying binomials multiply using FOIL First terms Outer terms Inner terms Last terms then add and combine like terms multiplying polynomials multiply each term in the first polynomial by each term in the next polynomial dividing polynomials use long division just like with numbers common forms of factoring factor common to all terms difference of squares squares of binomials factor common to all terms ax+ay=a(x+y) difference of squares a^2-b^2=(a-b)(a+b) square of binomials a^2+2ab+b^2=(a+b)^2 for unconventional factoring problems pick a couple numbers and plug them in the question and answers to see which ones come out the same Golden Rule of Equations Whatever you do to get the target variable or expression by itself, do the same thing to both sides. solving for an unknown in a denominator multiply by the denominator or cross multiply to remove the fractions solving for an unknown in an exponent re-express one or both sides so that the two sides have the same base, then you can pull out the exponent expressions and have them equal each other 8^x=16^(x-1) (2^3)^3=(2^4)^(x-1) 2^(3x)=2^(4x-4) 3x=4x-4 3x-4x=-4 -x=-4 x=4 Quadratic Equations 1. Write in this form: ax^2+bx+c=0 2. factor the left side 3. seat each factor to equal 0 4. solve each If the left side of a quadratic equation is not factorable, you can use the quadratic formula: x=(-b [+or-] sqrt[b^2-4ac])/2a "In terms of" equation solving multiple variables, solve for the variable in terms of the others 3x-10y=-5x+6y Solve for x in terms of y. -isolate x. simultaneous equations 4x+3y=8 and x+y=3, solve for x and y combine the equations so that one variable cancels out. (x+y)(-3)=3(-3) -3x-3y=-9 4x+3y=8 x=-1 -1+y=3 y=4 absolute value |x-12|=3 split the equation into two equations, then solve x-12=3 or x-12=-3 x= 15 or 9 absolute value and inequality isolate the variable. If you multiply or divide both sides by a negative, the sign must be switched to its opposite. If n>0 |whatever|0 |whatever|>n whatever<-n OR whatever>n |2x-3|<7 -7<2x-3<7 -4<2x<10 -27 (3x+9)/2<-7 OR (3x+9)/2>7