Question

Factorize the following:
$72x^6{y}^7-96x^7{y}^6$

Answer 1

Terms of the expression $(72x^6{y}^7-96x^7{y}^6)$ are $72x^6{y}^7\text{and}-96x^7{y}^6$

$72x^6{y}^7=3\times 3\times 8\times x^6\times y\times y^6$
$-96x^7{y}^6=-1\times 3\times 4\times 8\times x^6\times x\times y^6$

Greatest common factors $=3\times 8\times x^6\times y^6$
$=24x^6{y}^6$

$\therefore 72x^6{y}^7-96x^7{y}^6=24x^6{y}^6(3\times y-1\times 4\times x)$
$=24x^6{y}^6(3y-4x)$

Hence, the factorized form is $24x^6{y}^6(3y-4x)$.