# Distributive Property

The distributive property is a property used in Algebra where a number, when multiplied with a group of numbers, can be distributed to each number of the group and multiplied. Let’s look at the formula and examples for further explanations.

#### Distributive Property Formula –

$\LARGE a\times (b+c)=a\times b+a\times c$

### Solved Examples

Question 1: Solve 4(5 + 7), using distributive property.
Solution:

4(5 + 7)
using distributive property
4 $\times$ 5 + 4 $\times$ 7
=20 + 28
=48
Question 2: Solve (-2)(3x+5)
Solution:
(-2)(3x+5)
using distributive property
(-2)(3x)+(-2)(5)
= -6x-10

#### Practise This Question

Which of the following is true about multiplication of a vector by a scalar.

1) Scalar multiplication by a positive number other than 1 changes its magnitude but not direction.

2) Scalar multiplication always lead to change in magnitude and direction.

3) Scalar multiplication by -1 will not change the magnitude of the vector but will change its direction.

4) Scalar multiplication by a negative number other than -1 will reverse its direction and change its magnitude as well.