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