Distributive Property of Multiplication is one of the most important mathematical concepts for solving difficult multiplication. Calculations become easier to handle and comprehend when we divide the multiplication of a number among the addition or subtraction of other numbers thanks to this characteristic.

Not only is the distributive property crucial for fundamental arithmetic, but it also forms the basis for algebra and more advanced math.

What is Distributive Property of Multiplication?

Distributive Property of Multiplication is a rule that allows us to multiply a number by a sum or difference of numbers by distributing the multiplication to each term in the sum or difference. Mathematically, the distributive property is expressed as:

a × (b + c) = (a × b) + (a × c)

Accordingly, multiplying a by the product of b and c is equivalent to multiplying a by b and then adding the result to the product of a and c. The distributive property over subtraction is similarly stated as follows:

a × (b – c) = (a × b) – (a × c)

Because it makes calculations easier to understand and simplifies complicated formulas, the distributive property is a useful tool in mathematics. In algebra, it is frequently used to factor polynomials, solve equations, and enlarge and simplify statements.

Important Related Formulas/Concepts

Understanding the distributive property involves recognizing how it interacts with other mathematical operations and properties. Here are some related formulas and concepts:

Distributive Property Over Addition

a × (b + c) = (a × b) + (a × c)

This is the basic form of the distributive property, where multiplication is distributed over addition.

Distributive Property Over Subtraction

a × (b – c) = (a × b) – (a × c)

This form of the distributive property shows how multiplication is distributed over subtraction.

Combining Like Terms

After distributing, like concepts must frequently be combined when employing algebra’s distributive property:

a (b + c) + d (b + c) = (a + d) (b + c)

This helps in simplifying expressions and solving equations.

Distributive Property in Polynomial Multiplication

When multiplying polynomials, the distributive property helps to expand the product of two polynomials:

(a + b) (c + d) = ac + ad + bc + bd

Distributive Property of Multiplication-Worksheet

Question 1: Simplify the expression using the distributive property: 3 × (6 + 4).

Solution:

3 × (6 + 4)

= (3 × 6) + (3 × 4)

= 18 + 12

= 30

Question 2: Simplify the expression using the distributive property: 7 × (3 + 5).

Solution:

7 × (3 + 5)

= (7 × 3) + (7 × 5)

= 21 + 35

= 56

Question 3: Simplify the expression using the distributive property: 6 × (6 – 2).

Solution:

6 × (6 – 2)

= (6 × 6) + (6 × 2)

= 36 – 12

= 24

Question 4: Expand the expression using the distributive property: 4 (x + 3)

Solution:

4 (x + 3)

= (4 × x) + (4 × 3)

= 4x + 12

Question 5: Expand the expression using the distributive property: 7 (x – 2)

Solution:

7 (x – 2)

= (7 × x) – (7 × 2)

= 7x – 14

Question 6: Factor the expression using the distributive property: 12 + 8

Solution:

Factor of given expression:

12 + 8

= 4 (3 + 2)

Question 7: Factor the expression using the distributive property: 18-6

Solution:

18 – 6

= 6 (3 – 1)

Question 8: Simplify the expression using the distributive property: -3(2y + 5)

Solution:

-3(2y + 5)

= -3 × 2y + (-3) × 5

= -6y – 15

Question 9: Simplify the expression using the distributive property: 6(2x – 3y).

Solution:

6(2x – 3y)

= 6 × 2x – 6 × 3y

= 12x – 18y

Question 10: Find the value of x in given expression: 11x – 2 = 8x – 5

Solution:

11x – 2 = 8x – 5

11x – 8x = -5 + 2

3x = -3x

x = -3/3 = -1

Worksheet on Distributive Property of Multiplication

Worksheet on distributive property of multiplication is added below:

Answer Key

• Ans 1. 54
• Ans 2. 60
• Ans 3. 16
• Ans 4. 4x + 20
• Ans 5. 14 + 7y
• Ans 6. 8 (2 + 3)
• Ans 7. x = 4
• Ans 8. y = 6
• Ans 9. 12 + x
• Ans 10. 5a + 15b

Related Articles:

• Examples of Distributive Property in Real-Life
• Properties of Rational Numbers
• Properties of Integers

Frequently Asked Questions

What is Distributive Property of Multiplication?

Multiplying a number by the sum of two other numbers has the same effect as multiplying each number independently and then adding the results, according to the distributive property of multiplication. For example, a̗ (b + c) = (a × b) + (a × c).

Why is Distributive Property Important?

Distributive principle is a fundamental idea in algebra and higher-level mathematics, and it is significant because it makes complicated multiplication problems simpler. It facilitates the more effective breakdown and solution of equations.

Is it possible to Apply Distributive Property to Subtraction?

Yes, it is possible to use the distributive property to subtraction. For example, a×(b-c) = (a×b) – (a×c).

What is Algebraic use of Distributive Property?

Distributive property is a tool in algebra that helps with equation solving, term combination, and expression simplification. It is necessary for factoring and expanding expressions and makes algebraic expression manipulation simpler.