(3x 4y)^2 x^4 ⇒[(3x 4y)^2]^2 (x^2)^2 ⇒[(3x 4y)^2 x^2][(3x 4y)^2+x^2] ⇒[(3x 4y)+x][3x 4y x][(3x 4y)^2+x^2] ⇒(4x 4y)(2x 4y)[(3x 4y)^2+x^2 ...

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Formation of Algebraic Expressions

Solve: 3x -...

Question

Solve:
${(3 x - 4 y)}^{4} - x^{4}$

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Solution

${(3 x - 4 y)}^{2} - x^{4}$
$\Rightarrow {[{(3 x - 4 y)}^{2}]}^{2} - (x^{2})^{2}$
$\Rightarrow [{(3 x - 4 y)}^{2} - x^{2}] [{(3 x - 4 y)}^{2} + x^{2}]$
$\Rightarrow [(3 x - 4 y) + x] [3 x - 4 y - x] [{(3 x - 4 y)}^{2} + x^{2}]$
$\Rightarrow (4 x - 4 y) (2 x - 4 y) [{(3 x - 4 y)}^{2} + x^{2}]$
$\Rightarrow 8 (x - y) (x - 2 y) [9 x^{2} + 16 y^{2} - 24 x y + x^{2}]$
$\Rightarrow 16 (x - y) (x - 2 y) [5 x^{2} + 8 y^{2} - 12 x y]$

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