Question

Factorize $2(x+2y)^{2} - 5(x+2y)+2$

Answer 1

$\tt{2(x + 2y)^{2} - 5(x + 2y) + 2}$

Using binomial theorem,

$\tt\small{ = 2(x^{2} + 2xy + {y}^{2}) - 5(x + 2y) + 2}$

Using distributive property,

$\tt\small{ = 2 {x}^{2} + 4xy + 2 {y}^{2} - 5(x + 2y)}$

$\sf\small{ = 2 {x}^{2} + 4xy + 2 {y}^{2} - 5x - 10y + 2}$

Answer 2

Step-by-step explanation:

$let \: x + 2y \: = a \: then \: \\ \\ 2a {}^{2} - 5a + 2 \\ = 2a {}^{2} - a \: - 4a \: + 2 \\ = a(2a - 1) - 2(2a - 1) \\ = (2a - 1) \: \: (a - 2) \\ = (2(x + 2y \: - 1) \: (x + 2y \: ) \: - 2) \\ = (2x + 4y - 2) \: (x + 2y \: - 2)$

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