Deck 1 Flashcards
Distributive Law
a(b + c) = ab + ac
Addition is still linked for fractions, not multiplication.
Associative Law
(a + b) + c = a + (b + c)
(ab)c = a(bc)
sqrt(abc) = sqrt(ab) x sqrt(c)
Addition is still linked for fractions, not multiplication.
Commutative Law
a + b = b + a
ab = ba
Less traditional, but important: a - b = - b + a But a - b doesn’t = b - a 5 * 1/10 = 1/10 * 5 But 5/10 doesn’t = 10/5 (Obviously)
Addition is still linked for fractions, not multiplication.
(a + b)^2
a^2 + 2ab + b^2
(a - b)^2
a^2 - 2ab + b^2
ab + ac
a(b + c)
(a + b) + c
a + (b + c)
(ab)c
a(bc)
(a - b) (a + b)
a ² - b ²
Use the Distributive Law to find three equivalents of:
a / b) + (c / b
1) 1/b x a + 1/b x c
2) 1/b (a + c)
3) a + c / b
Polynomial parts
5X² + 3
A polynomial is a sum of terms made up of coefficients multiplying a variable with an exponent that is a non-negative integer [0,inf)
Term = 5x² and 3
Coefficient = the numbers
Constant = the coefficient(s) by itself with no variable, which is technically x^0.
E.g., 3 = 3x^0
Difference of squares formula
a² - b ² = (a + b) (a - b)
Prime factorization
3
Add digits together
If the sum is a multiple of 3, the original number is
Prime factorization steps
Look for lowest prime factors
Draw tree
Take final leaves of tree as prime factor
sqrt(abc)
sqrt(ab) x sqrt(c)
ORDER OF OPERATIONS
P E M, D A, S IF THEY FIGHT, LEFT TO RIGHT!
Multiplication & division are the same level.
Addition & subtraction are the same level.
Multiplying polynomials
In general, when multiplying two polynomials together, use the distributive property, until every term of one polynomial is multiplied times every term of the other polynomial. Make sure that you simplify your answer by combining any like terms.
GCF process
Build a factor tree and take the product of all common prime factors.
