Question

Factorize each of the following expression:
(3x + 4y)⁴ − x⁴

Answer 1

\[(3x + 4y )^4 - x^4 \]
\[ = [(3x + 4y )^2 ]^2 - ( x^2 )^2 \]
\[ = [(3x + 4y )^2 + x^2 ][(3x + 4y )^2 - x^2 ]\]
\[ = [(3x + 4y )^2 + x^2 ][(3x + 4y) + x][(3x + 4y) - x]\]
\[ = {(3x + 4y )^2 + x^2 }(3x + 4y + x)(3x + 4y - x)\]
\[ = \left\{ \left( 3x + 4y \right)^2 + x^2 \right\}(4x + 4y)(2x + 4y)\]
\[ = \left\{ \left( 3x + 4y \right)^2 + x^2 \right\}4(x + y)2(x + 2y)\]
\[ = 8\left\{ \left( 3x + 4y \right)^2 + x^2 \right\}(x + y)(x + 2y)\]