Algebraic Formulae

Question 1

x^2 - y^2

Answer 1

(x + y)(x - y)

Question 2

x^3 +/- y^3

Answer 2

(x +/- y)(x^2 -/+ xy + y^2)

Question 3

(x +/- y)^2

Answer 3

x^2 +/- 2xy + y^2

Question 4

(x +/- y)^3

Answer 4

x^3 +/- 3x^2y + 3xy^2 +/- y^3

Question 5

x^0

Answer 5

1, if x does not = 0

Question 6

x^1

Answer 6

x

Question 7

x^-n

Answer 7

1/x^n if x does not = 0

Question 8

x^m . x^n

Answer 8

x^(m+n)

Question 9

(x^m)^n

Answer 9

x^(mn)

Question 10

x^m / x^n

Answer 10

x^(m-n) if x does not = 0

Question 11

(x.y)^m

Answer 11

x^m . y^m

Question 12

(x/y)^n

Answer 12

x^n / x^y

Question 13

x^(m/n)

Answer 13

nrt(x^m) if a is >/= 0, m>/= 0, n >/= 0

Question 14

y = log(a)x

Answer 14

x = a^y where a>0, a does not = 0

Question 15

a^(log(a)M)

Answer 15

m

Question 16

log(a)M^x

Answer 16

xlog(a)M

Question 17

log(a)(M.N)

Answer 17

log(a)M + log(a)N

Question 18

log(a)(M/N)

Answer 18

log(a)M - log(a)N

Question 19

log(a)M

Answer 19

log(b)M/log(b)a = logM/loga = lnM/lna = log(10)M/log(10)a

Question 20

log(a)a

Answer 20

1 if a>0

Question 21

log(a)1

Answer 21

0 if a>0

Question 22

log(e)x

Answer 22

lnx

Question 23

ln(xy)

Answer 23

lnx + lny

Question 24

ln(x/y)

Answer 24

lnx - lny

Question 25

lnx^y

Answer 25

ylnx

Question 26

lne^x

Answer 26

x if x>0

Question 27

e^(lnx)

Answer 27

x

Question 28

lne

Answer 28

1

Question 29

ln1

Answer 29

0

Question 30

e^x = e^y

Answer 30

x = y

Question 31

lnx = lny

Answer 31

x = y

Question 32

a^b = z

Answer 32

lnz = blna –> b = lnz/lna

Question 33

a^(lnb)

Answer 33

b^(lna)

Question 34

(a/b)/(c/d)

Answer 34

ad/bc

Question 35

Quadratic Equation

Answer 35

ax^2 + bx + c = 0, where a, b, c are constants and a does not equal 0.

Question 36

Quadratic Formula

Answer 36

[-b +/- sqrt(b^2 - 4ac)]/2a = x (root)

Question 37

Inverse

Answer 37

f(g(x)) = x, then g(x) = f^(-1)(x). Switch x and y.