x^4 (y + z)^4 ⇒ (x^2)^2 ((y+z)^2)^2 a^2 + b^2 = (a+b)(a b) ⇒ [x^2 + (y + z)^2] [x^2 (y + z)^2] ⇒ [x^2 + (y + z)^2] [(x+y+z) (x y ...

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(a-b)^2 Expansion and Visualisation

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Question

Solve :
$x^{4} - (y + z)^{4}$

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Solution

$x^{4} - (y + z)^{4}$

$\Rightarrow (x^{2})^{2} - ((y + z)^{2})^{2}$

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

$\Rightarrow [x^{2} + (y + z)^{2}] [x^{2} - (y + z)^{2}]$

$\Rightarrow [x^{2} + (y + z)^{2}] [(x + y + z) (x - y - z)]$

$\Rightarrow [x^{2} + y^{2} + z^{2} + 2 y z] [(x + y + z) (x - y - z)]$

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