Algebra

Question 1

Multiplying powers with same base

Answer 1

to multiply with the same base, keep the base and add the exponents

Question 2

Dividing Powers with the same base

Answer 2

to divide powers with the same base keep the base and subtract the exponents

Question 3

raising a power to an exponent

Answer 3

to raise a power to an exponent keep the base an multiply the exponents

Question 4

multiplying powers with same exponent

Answer 4

to multiply powers with the same exponent multiply the base and keep the exponent

Question 5

dividing powers with the same exponent

Answer 5

to divide powers with the same exponent, divide the bases and keep the exponent

Question 6

combining like terms

Answer 6

to combine like terms keep the variable part unchanged while adding or subtracting the coefficient

Question 7

multiplying monomials

Answer 7

to multiply monomials multiply the coefficients and the variables separately

Question 8

multiplying binomials

Answer 8

to multiply binomials use foil. then combine like terms

Question 9

multiplying polynomials

Answer 9

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

Question 10

after multiplying polynomials

Answer 10

you should end up with the number of terms of the product of polynomial one and two. before simplifying.

Question 11

Dividing polynomials

Answer 11

set it up in long division and take it term by term

Question 12

Factor to all common terms

Answer 12

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).

Question 13

Difference of squares

Answer 13

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)

Question 14

Squares of binomials

Answer 14

learn to recognize polynomials that are squares of binomials.
a^2+2ab+b^2= (a+b)^2

Question 15

Factoring a quadratic expression

Answer 15

think about what binomials you could use FOIL to get that quadratic expression. (factor out then simplify)

Question 16

The golden rule of solving algebra equations

Answer 16

do the same thing to both sides

Question 17

solving the unknown in the denominator

Answer 17

do the same thing to both sides. in this case you multiply to undo division. you can also cross multiply

Question 18

unknown in the exponent

Answer 18

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

Question 19

alternative method to unknown exponent

Answer 19

solve it backwards, using answer choices to plug in

Question 20

solving quadratic equations

Answer 20

to solve put the equation in ax^2+bx+c=0 then factor the left side if possible. if not use the quadratic formula.

Question 21

solving an unknown equation in terms of

Answer 21

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.

Question 22

simultaneous equations

Answer 22

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.

Question 23

absolute value

Answer 23

think of the two different cases. for example a negative answer equation and a positive answer equation.

Question 24

to solve an inequality

Answer 24

do whatever is necessary to both sides to isolate the variable. just remember when you multiply and divide both sides reverse the sign.

Question 25

to solve an absolute inequality

Answer 25

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 .