Answer
Chapter 6 - Section 6.2 - Exercise Set: 61 (Answer)
$5x^3y - 25x^2y^2 - 120xy^3$ = $5xy(x + 3y)(x - 8y)$
Work Step by Step
Chapter 6 - Section 6.2 - Exercise Set: 61 (Solution)
Factorize : $5x^3y - 25x^2y^2 - 120xy^3$
First step : Take out the GCF of $5x^3y$, $25x^2y^2$ and $120xy^3$ which is $5xy$
$5x^3y - 25x^2y^2 - 120xy^3$ = $5xy(x^2 - 5xy - 24y^2)$
Take $(x^2 - 5xy - 24y^2)$ to be $(x + \triangle y)(x + \square y)$
For this, we have to look for two numbers whose product is -24 and whose sum is -5.
Factors of -24 $\Longleftrightarrow$ Sum of Factors
1,-24 $\Longleftrightarrow$ -23 (Incorrect sum)
2,-12 $\Longleftrightarrow$ -10 (Incorrect sum)
3,-8 $\Longleftrightarrow$ -5 (Correct sum, so the numbers are 3 and -8)
4,-6 $\Longleftrightarrow$ -2 (Incorrect sum)
6,-4 $\Longleftrightarrow$ 2 (Incorrect sum)
… more trials but not necessary as 3,-8 met the criteria already
Thus, $5x^3y - 25x^2y^2 - 120xy^3$ = $5xy(x + 3y)(x - 8y)$
