Distributive Property of Division

We can divide larger numbers using the distributive property by breaking those numbers into smaller factors.

Let us see an example here:

Q: Divide 84 ÷ 6.

We can write 84 as 60+24

Hence,

(60 + 24) ÷ 6

Now distributing division operation for each factor in the bracket we get;

(60 ÷ 6) + (24 ÷ 6)

= 10 + 4

= 14

Examples

Example 1:

Solve the given expression using the distributive property:

(i) 4(2x⁴+ 7x)

(ii) 2x(x²+ y)

(iii) 4(7xy+ 13yx)

Solution:

According to the distributive property,

A ( B + C) = AB + AC

(i) 4(2x⁴+ 7x)

Using distributive law we have,

= 4. 2x⁴+ 4. 7x

= 8x⁴+ 28x

(ii) 2x(x²+ y)

Using Distributive property,

= 2x .  x²  + 2x. y

= 2x³+ 2xy

(iii) 4(7xy+ 13yx)

Using distributive property, we have

= 4. 7xy + 4. 13yx

= 28 xy + 52 xy

= 80 xy

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