how do i factorise these expressions?

a² - b² = (a - b) * (a + b)

<=>

x² - 81 = (x - 9) * (x + 9)

because a² = x² so a = x

and

b² = 81 so b = 9

*******

x² - 64 = (x - 8) * (x + 8)

because

a² = x² so a = x

and

b² = 64 so b = 8

a^2 - b^2 = (a + b)(a - b)

1)
x^2 - 81
= x^2 - 9^2
= (x + 9)(x - 9)

2)
x^2 - 64
= x^2 - 8^2
= (x + 8)(x - 8)

Using the formula:
a² - b² = (a - b)(a + b)

x² - 81
= x² - 9²
= (x - 9)(x + 9)

x² - 64
= x² - 8²
= (x - 8)(x + 8)

Done

a^2-b^2=(a-b)(a+b)
b=9
b=8

You are after this.

( x - a )( x + a ) = x² - a²

x² - 81 => Guess the value of a ?

a = 9 => ( x - 9 )( x + 9 )

x² - 64 => Guess the value of a ?

a = 8 => ( x - 8 )( x + 8 )


Works for others as well, you can create your own questions...

x² - 144 => Guess the value of a ?

a = 12 => ( x - 12 )( x + 12 )

etc...

(x-9)*(x+9)
(x-8)*(x+8)

x^2 is a square number, it is x squared. 81 and 64 are also square numbers, 9 and 8 squared respectively. The method used to factorize the expressions is known as 'Difference of Two Squares'.

x^2-81 = (x-9)(x+9) since the +9x and -9x will cancel out.

The same method can be used to factorize x^2-64.

x^2-81=

take the square root of both. x^2 = x 81>9

answer is (x + 9) (x - 9)


x^2-64=

do the same. You can only use this method if you are subtracting the 2 numbers.

answer is (x +8) (x-8)