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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.
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.
Understanding the distributive property involves recognizing how it interacts with other mathematical operations and properties. Here are some related formulas and concepts:
a × (b + c) = (a × b) + (a × c)
This is the basic form of the distributive property, where multiplication is distributed over addition.
a × (b - c) = (a × b) - (a × c)
This form of the distributive property shows how multiplication is distributed over subtraction.
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.
When multiplying polynomials, the distributive property helps to expand the product of two polynomials:
(a + b) (c + d) = ac + ad + bc + bd
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 is added below:
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