How do you factor the trinomial $4 x^{2} + 20 x + 25$ ?

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Solution

Factorizing the given expression:
Given,
The expression is $4 x^{2} + 20 x + 25$
Multiplying $4 & 25$ we get $100$ .
Finding two numbers such that when we add them we get $20$ and when we multiply them get $100$ .
The required numbers are $= 10, 10$
Therefore, we can write
$\Rightarrow 4 x^{2} + 10 x + 10 x + 25 \Rightarrow 2 x (2 x + 5) + 5 (2 x + 5) \Rightarrow (2 x + 5) (2 x + 5)$
Hence, the factors of $4 x^{2} + 20 x + 25$ are $(2 x + 5) (2 x + 5)$ .

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