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Multiplication of Any Polynomial

Expand : 4x...

Question

Expand : $(4 x + 1) (4 x - 1)$

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Solution

$(4 x + 1) (4 x - 1)$
$\Rightarrow 4 x (4 x - 1) + 1 (4 x - 1)$
$\Rightarrow (4 x) (4 x) - (4 x) (1) + 1 (4 x) + 1 (- 1)$
$\Rightarrow 16 x^{2} - 4 x + 4 x - 1$
$\Rightarrow 16 x^{2} - 1$
$∴ (4 x + 1) (4 x - 1) = (16 x^{2} - 1) = (4 x)^{2} - (1)^{2}$ .

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Q. Explain and expand the identity geometrically:

(4 x + 1) (4 x + 5)

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