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)
