Question

a²-b² expand. cite examples. What type of equation is this, explain where it is used

a power n -b power has a factor only if n is_______

Answer 1

first of all you know this is not a equation this is an identity okay .

now,
here degree of ( a² -b²) is two . so, this is quadratic identity . hence, it have two zeros .
now,
according to basic algebra
a² - b² = ( a - b)( a + b)

if a² - b² = 0 then this is an equation ,
now,
a² - b² =( a - b) ( a - b) =0
a = b , - b

here you can see there are two value a
hence it is correct this is quadratic identity .

now,
example :-
this is soul of mathematics ,because application of this frquently used in Algebra, trigo, calculus , geometry etc .
also this expression help in some branches of physics , chemistry .

in Algebra :-
given , two large number 105 , 110
in this form.
110² - 105² = ? so, tough for finding directly but when we use , basic rule the we can easily find out .
110² -105² =(110+105)(110-105) = 215×5
= 1075 .
so, in this way you can use in algebra .

for finding of zeros of quadratic equation , this is most helpful .
see this
ex :- x² -25 =0 find zeros ?

x² -5²= 0

( x -5)( x + 5) = 0
x = 5 , -5

in this way we use this expression .

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aⁿ - bⁿ this is also an expression ,( nth degree expression)

if n = 1 then it has a factor only .

due to a¹ - b¹ = 1( a - b)
it has a factor that is 1

Answer 2

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