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Introduction to Algebraic Identities

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, $(3 x - 4 y) (3 x + 4 y) (9 x^{2} + 16 y^{2})$ .

We know, $(a + b) (a - b)$ $= (a^{2} - b^{2})$ .

Multiply by using direct method, we get,
$(3 x - 4 y) (3 x + 4 y) (9 x^{2} + 16 y^{2})$ $= [(3 x)^{2} - (4 y)^{2}] (9 x^{2} + 16 y^{2})$
$= (9 x^{2} - 16 y^{2}) (9 x^{2} + 16 y^{2})$ $= (9 x^{2} + 16 y^{2}) (9 x^{2} - 16 y^{2})$ .
Now, by using formula $(a^{2} - b^{2}) = (a + b) (a - b)$ , we get,
$= ((9 x^{2})^{2} - (16 y^{2})^{2})$
$= 81 x^{4} - 256 y^{4}$ .

Hence, the statement is true.
Therefore, $1$ is the correct answer.

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