Question

Factorise :- a 8 + b 8

Answer 1

Answer:

-a⁸ + b⁸ = (b⁴ + a⁴)(b² + a²)(b + a)(b - a)

Step-by-step explanation:

Factorise :- a 8 + b 8

-a⁸ + b⁸

= b⁸ - a⁸

= (b⁴)² - (a⁴)²

Using x² - y² = ( x+ y)(x -y)

here x = b⁴ & y = a⁴

= (b⁴ + a⁴)(b⁴ - a⁴)

= (b⁴ + a⁴)( (b²)² - (a²)²)

= (b⁴ + a⁴)(b² + a²)(b² - a²)

= (b⁴ + a⁴)(b² + a²)(b + a)(b - a)

-a⁸ + b⁸ = (b⁴ + a⁴)(b² + a²)(b + a)(b - a)

Answer 2

Answer:

$-a^{8}+b^{8}\\=(b^{4}+a^{4})(b^{2}+a^{2})(a+b)(b-a)$

Step-by-step explanation:

$Given \: -a^{8}+b^{8}$

$=b^{8}-a^{8}\\=(b^{4})^{2}-(a^{4})^{2}$

/* We know the algebraic identity:

x²-y²=(x+y)(x-y) */

$=(b^{4}+a^{4})(b^{4}-a^{4})$

$=(b^{4}+a^{4})[(b^{2})^{2}-(a^{2})^{2}]\\=(b^{4}+a^{4})(a^{2}+b^{2})(b^{2}-a^{2})\\=(b^{4}+a^{4})(b^{2}+a^{2})(b+a)(b-a)$

Therefore,

$-a^{8}+b^{8}\\=(b^{4}+a^{4})(b^{2}+a^{2})(a+b)(b-a)$

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