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(a + b)^2 Expansion and Visualisation

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Question

Expand using binomial identity.
$(2 x + 5)^{2}$

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Solution

$(2 x + 5)^{2}$
$= (2 x)^{2} + 5^{2} + 2 \cdot 2 x \cdot 5$ $[(a + b)^{2} = a^{2} + b^{2} + 2 a b]$
$= 4 x^{2} + 25 + 20 x$
$= 4 x^{2} + 20 x + 25$
$∴ (2 x + 5)^{2} = 4 x^{2} + 20 x + 25$

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