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(a+b)(a-b) Expansion and Visualisation

Evaluate: 3x...

Question

Evaluate:
$(3 x + 4 y) (3 x - 4 y) (9 x^{2} + 16 y^{2})$ is equal to $81 x^{4} - 256 y^{4}$ .
If true then enter $1$ and if false then enter $0$

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Solution

Given, $(3 x + 4 y) (3 x - 4 y) (9 x^{2} + 16 y^{2})$
Applying the formula $(a + b) (a - b) = a^{2} - b^{2}$ , where $a = 3 x, b = 4 y$
$(3 x + 4 y) (3 x - 4 y) (9 x^{2} + 16 y^{2}) = ({9 x}^{2} - {16 y}^{2}) (9 x^{2} + 16 y^{2})$
$= (9 x^{2})^{2} - (16 y^{2})^{2}$
$= (81 x^{4} - 256 y^{4})$

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