Question

(iii) x8-16y8
Find the answer

Answer 1

The value of $x^{8}$ - 16$y^{8}$ is

"($x^{4}$ + 4$y^{4}$) × ($x^{2}$ + 2y)($x^{2}$ - 2y)".

Step-by-step explanation:

We have:

$x^{8}$ - 16$y^{8}$

= $(x^{4} )^{2}$ - $(4y^{4}) ^{2}$

= ($x^{4}$ + 4$y^{4}$) × ($x^{4}$ - 4$y^{4}$)

[ Since, (a + b)(a - b) = $a^{2}$ - $b^{2}$ )

= ($x^{4}$ + 4$y^{4}$) × ($(x^{2}) ^{2}$ -$(2y)^{2}$)

= ($x^{4}$ + 4$y^{4}$) × ($x^{2}$ + 2y)($x^{2}$ - 2y)

Hence, the value of $x^{8}$ - 16$y^{8}$ is

($x^{4}$ + 4$y^{4}$) × ($x^{2}$ + 2y)($x^{2}$ - 2y).

Answer 2

Answer:

x^8-16y^8

=(x^4)^2-(4y^4)^2

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

={(x^2+2y^2)^2-4x^y^2}{(x^2)^2-(2y^2)^2}

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

Now this cannot be factories further.So, this is ur final answer child.