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Factorize (p+q)^2-20 (p+q)-125....

Factorize `(p+q)^2-20 (p+q)-125`.

Text Solution

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The given expression is `(p+q)^2-20 (p+q)-125`.
Putting `(p+q) =x`, it becomes `x^2-20x-125`.
We split -20 into two parts whose sum is -20 and product -125.
Clearly, ` (-25+5)=-20 and (-25)xx 5 =-125`
`therefore x^2-20-125=x^2-25=x^2-25x+5x-125`
` =x(x-25)+5(x-25)`
` =9x-25)(x+5)`.
`therefore (p+q)^2-20(p+q)-125 =(p+q-25)(p+q+5)" "[because x=p+q]`.
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