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Introduction to Square Numbers

Evaluate: 3-...

Question

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

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Solution

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

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

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

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

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