Algebra Flashcards
Multiplying powers with same base
to multiply with the same base, keep the base and add the exponents
Dividing Powers with the same base
to divide powers with the same base keep the base and subtract the exponents
raising a power to an exponent
to raise a power to an exponent keep the base an multiply the exponents
multiplying powers with same exponent
to multiply powers with the same exponent multiply the base and keep the exponent
dividing powers with the same exponent
to divide powers with the same exponent, divide the bases and keep the exponent
combining like terms
to combine like terms keep the variable part unchanged while adding or subtracting the coefficient
multiplying monomials
to multiply monomials multiply the coefficients and the variables separately
multiplying binomials
to multiply binomials use foil. then combine like terms
multiplying polynomials
to multiply polynomials with more than two terms, make sure you multiply each term in the first polynomial by each term in the second. (FOIL only works when using two binomials
after multiplying polynomials
you should end up with the number of terms of the product of polynomial one and two. before simplifying.
Dividing polynomials
set it up in long division and take it term by term
Factor to all common terms
this is essentially the distributive property in reverse. For example all three terms 3x^3+ 12x^2-6x all have 3x in them. pulling out the common factor is 3x(x^2+4x-2).
Difference of squares
when ever you have two identifiable squares with a minus sign between them, you can factor the expression like this: a^2-b^2=(a+b)(a-b)
Squares of binomials
learn to recognize polynomials that are squares of binomials.
a^2+2ab+b^2= (a+b)^2
Factoring a quadratic expression
think about what binomials you could use FOIL to get that quadratic expression. (factor out then simplify)
The golden rule of solving algebra equations
do the same thing to both sides
solving the unknown in the denominator
do the same thing to both sides. in this case you multiply to undo division. you can also cross multiply
unknown in the exponent
reexpress both sides of the eqauation so that the two sides have the same base. now that both sides have the same base you can simply set the exponent expressions equal and solve for x
alternative method to unknown exponent
solve it backwards, using answer choices to plug in
solving quadratic equations
to solve put the equation in ax^2+bx+c=0 then factor the left side if possible. if not use the quadratic formula.
solving an unknown equation in terms of
meaning more than one variable. isolate the variable on one side of the equation, leaving an expression containing the other variable on the other side of the equation.
simultaneous equations
you can solve for two variables only if you have two distinct equations. two forms of the same equations will not work. combine the equations in such a way that one of the variables cancels out. you can also just add the two equations then simplify.
absolute value
think of the two different cases. for example a negative answer equation and a positive answer equation.
to solve an inequality
do whatever is necessary to both sides to isolate the variable. just remember when you multiply and divide both sides reverse the sign.
to solve an absolute inequality
to solve an inequality in form [whatever] < p, where p> 0, just put that “whatever” inside the range of -p to p.
if [“w”] >p then put it outside the range of -p and p .
