Factorize $2 x^{2} - 5 x y + 3 y^{2}$ and use your result to factorize $2 {(3 a - b)}^{2} - 5 (3 a - b) (2 a - b) + 3 {(2 a - b)}^{2}$ . The factors are

a^{2} b

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(a + b) (a - b)

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a b

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(2 a + b) (a - b)

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Solution

The correct option is C $a b$
Let us factorize $2 x^{2} - 5 x y + 3 y^{2}$ as shown below:
$2 x^{2} - 5 x y + 3 y^{2} = 2 x^{2} - 2 x y - 3 x y + 3 y^{2} = 2 x (x - y) - 3 y (x - y) = (2 x - 3 y) (x - y)$
Substitute $x = (3 a - b)$ and $y = (2 a - b)$ in $(2 x - 3 y) (x - y)$ as follows:
$(2 x - 3 y) (x - y) = [2 (3 a - b) - 3 (2 a - b)] [(3 a - b) - (2 a - b)] = (6 a - 2 b - 6 a + 3 b) (3 a - b - 2 a + b) = b \times a = a b$
Hence, the factors are $a b$ .

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