Factorise: ${(5 x - 3)}^{2} - (5 x - 3) - 20$

(5 x + 8) (5 x - 1)

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(5 x - 8) (5 x + 1)

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(5 x - 8) (5 x - 1)

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(5 x + 8) (5 x + 1)

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Solution

The correct option is B $(5 x - 8) (5 x + 1)$
${(5 x - 3)}^{2} - (5 x - 3) - 20$
Let $(5 x - 3) = a$ . Then, the expression becomes
$a^{2} - a - 20 = a^{2} - 5 a + 4 a - 20$
$= a (a - 5) + 4 (a - 5) = (a - 5) (a + 4)$
$= (5 x - 3 - 5) (5 x - 3 + 4)$
$= (5 x - 8) (5 x + 1)$

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