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) $(-57)\times (-19)+57$

Solution:

To find the product using suitable properties, we use the Distributive Law of Multiplication over Addition, which states:

a × (b + c) = (a × b) + (a × c)

Let us apply this property to simplify the given expression:

Given expression: 26 × (-48) + (-48) × (-36)

Here, let a = -48, b = 26, and c = -36. Substituting these values into the property:

a × b + a × c = a × (b + c)

So, -48 × 26 + -48 × -36 = -48 × (26 - 36).

Simplify the terms inside the parentheses:

-48 × (26 - 36) = -48 × (-10)

Now multiply the numbers:

-48 × -10 = 480

Thus, the product of the given expression, when solved using suitable properties, is: 480