Question
Factories: $(x^2- 3x)(x^2- 3x - 1) - 20.$
✓
Answer
$(x^2- 3x)(x^2- 3x - 1) - 20$
$= (x^2- 3x)[(x^2- 3x) - 1] - 20$
$= a[a - 1] - 20 ….( $Taking $x^2 - 3x = a )$
$= a^2- a - 20$
$= a^2- 5a + 4a - 20$
$= a(a - 5) + 4(a - 5)$
$= (a - 5)(a + 4)$
$= (x^2- 3x - 5)(x^2- 3x + 4)$
$= (x^2- 3x)[(x^2- 3x) - 1] - 20$
$= a[a - 1] - 20 ….( $Taking $x^2 - 3x = a )$
$= a^2- a - 20$
$= a^2- 5a + 4a - 20$
$= a(a - 5) + 4(a - 5)$
$= (a - 5)(a + 4)$
$= (x^2- 3x - 5)(x^2- 3x + 4)$
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