Question

factorise each of the following algebraic expression.
please help me
I will give 12 thanks plus follow​

Answer 1

Answer:

$= {x}^{8} - 1 \\ = {( {x}^{4}) }^{2} - {1}^{2} \\ = ( {x}^{4} - 1)( {x}^{4} + 1) \\ = (( { {x}^{2}) }^{2} - 1)( {x}^{4} + 1) \\ = ( {x}^{4} + 1)( {x}^{2} + 1)( {x}^{2} - 1) \\ = ( {x}^{4} + 1)( {x}^{2} + 1)(x + 1)(x - 1) \\ \\ \\ = {x}^{2} + 8x + 15 \\ = {x}^{2} + 5x + 3x + 15\\ = x(x + 5) + 3(x + 5) \\ = (x + 5)(x + 3) \\ \\ \\ \\ = {x}^{4} + 4 \\ = { ({x}^{2} )}^{2} + {2}^{2} \\ = ( {x}^{2} + 2)( {x}^{2} - 2) \\ = ( {x}^{2} + 2)( {x}^{2} + \sqrt{2} )( {x}^{2} - \sqrt{2} )$

Answer 2

Explanation:

1.x^8-1

=(x^4+1) (x^4-1)

=(x^4+1) (x^2+1) (x^2-1)

=(x^4+1) (x^2+1) (x+1) (x-1)

2.x^2+8x+15

=(x+3) (x+5)

=if,x+3=0

then,x=-3

=if,x+5=0

then,x=-5

3.x^4+4

=x^2+2^2

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

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