Question
Factorize:
$(x + 2)(x^2 + 25) - 10x^2 - 20x$
$(x + 2)(x^2 + 25) - 10x^2 - 20x$
✓
Answer
$(x + 2)(x^2 + 25) - 10x^2 - 20x (x + 2)(x^2 + 25) - 10x (x + 2)$
Taking (x + 2) common in both the terms =$ (x + 2)(x^2 + 25 - 10x)$
$= (x + 2)(x^2 - 10x + 25)$
Splitting the middle term of
$(x^2 - 10x + 25)$
$= (x + 2)(x^2 - 5x - 5x + 25)$
$= (x + 2){x(x - 5)-5 (x - 5)}$
$= (x + 2)(x - 5)(x - 5)$
$\therefore$ $(x + 2)(x^2 + 25) - 10x^2 - 20x = (x + 2)(x - 5)(x - 5)$
Taking (x + 2) common in both the terms =$ (x + 2)(x^2 + 25 - 10x)$
$= (x + 2)(x^2 - 10x + 25)$
Splitting the middle term of
$(x^2 - 10x + 25)$
$= (x + 2)(x^2 - 5x - 5x + 25)$
$= (x + 2){x(x - 5)-5 (x - 5)}$
$= (x + 2)(x - 5)(x - 5)$
$\therefore$ $(x + 2)(x^2 + 25) - 10x^2 - 20x = (x + 2)(x - 5)(x - 5)$
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