Question

Find the product, using suitable properties:

(a) $26\times (-48)+(-48)\times (-36)$

(b) $8\times 53\times (-125)$

(c) $15\times (-25)\times (-4)\times (-10)$

(d) $(-41)\times 102$

(e) $625\times (-35)+(-625)\times 65$

(f) $7\times (50-2)$

(g) $(-17)\times (-29)$

(h) $(-57)\times (-19)+57$

Answer 1

(a) $26\times (-48)+(-48)\times (-36)$

$=(-48)\times 26+(-48)\times (-36)$ [Using Commutative Property]

$=(-48)[26-36]$ [Using Distributive Property]

$=(-48)\times (-10)=480$

(b) $8\times 53\times (-125)=8\times [53\times (-125\left)\right]$

= $[8\times (-125\left)\right]\times 53$ [Using Associative Property]

= $[-1000]\times 53=-53000$

(c) $15\times (-25)\times (-4)\times (-10)$

= $15\times \left[\right(-25)\times (-4\left)\right]\times (-10)$ [Using Associative Property]

= $15\times \left[100\right]\times (-10)$

= $15\times (-1000)=-15000$

(d) $(-41)\times 102$

= $(-41)\times (100+2)$

= $(-41)\times 100+(-41)\times 2$ [Using Distributive Property]

= $-4100-82=-4182$

(e) $625\times (-35)+(-625)\times 65$

= $625\times \left[\right(-35)+(-65\left)\right]$ [Using Distributive Property]

= $625\times [-100]=-62500$

(f) $7\times (50-2)$

= $(7\times 50)-(7\times 2)$ [Using Distributive Property]

=$350-14$

= $336$

(g) $(-17)\times (-29)$

= $(-17)\times [-30+1]$

=$\left[\right(-17)\times (-30\left)\right]+\left[\right(-17)\times 1]$ [Using Distributive Property]

= $\left[510\right]+[-17]=493$

(h) $(-57)\times (-19)+57$

=$57\times 19+57\times 1$ [Using Distributive property]

=$57[19+1]$

=$57\times 20=1140$