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Distributive Properties

Word distribution in Algebra means breaking. We also call the distributive property as distribution law. By distributive property definition, we Mean “to separate“ or “to break into parts”.
In algebra when we say we are applying distributive properties, we mean we are expanding the given expression or we are distributing the terms of the given expression.
By distributive definition in Algebra:
We have distribution with respect to addition, according to which we say:
 a ( b + c ) = a * b   + a * c,
Or we can say that here we multiply term ‘b’ with ‘a’ and then term ‘c’ with term ‘a’. Now the relation of addition is formed between the two terms which are ‘ab’ and ‘ac’.
We also have distribution with respect to subtraction, according to which we say:
 a ( b - c ) = a * b   -  a * c,
Or we can say that here we multiply term ‘b’ with ‘a’ and then term ‘c’ with term ‘a’. Now the relation of subtraction is formed between the two terms which are ‘ab’ and ‘ac'.
Various algebraic expressions can be solved by using the distributive property and we get the factors of the given expressions.
Suppose the expression ax2 +bx2 is given. We observe that x2 is the common factor among the two given terms. So we bring out the common term from both the factors and express it as:
x2  * ( a  + b ) Ans.
Similarly various algebraic identities are also solved based on distributive property.
Let us take (a + b) (a – b),
It is written as a (a - b ) + b ( a – b ),
Here first term (a – b) is multiplied by ‘a’ and then the same term is multiplied by ‘b’. Now by applying distributive property, we get:  a * a – a * b + a * b – b * b.
    Or we write it as a2 - ab + ab – b2,
                  = a2  –  b2,
Thus we get the identity a2  –  b2  =   ( a + b ) ( a – b ).
Various multiplication sums in algebra are simplified using the distributive property.
Example: ( 4x * 2 ) + ( 3 * 2 ) is to be solved, we observe that  2 is common in both the braces, thus we bring out 2 and we get:
2 * ( 4x + 3 ) as the solution.

Associated calculator of Distributive Properties

Using distributive property solve the equation 6(2 + 3)?

When we solve any equation by using distributive property then product and sum of number is equals to individual sum of product that is,
 m (n + o)= m(n) + m(o),
m (n + o)= mn + mo.
This property is very useful with mental Math. Now we can solve the given equation by using distributive property,
Step1: 6 (2 + 3) = 6(2) + 6(3),
Step2: Let us consider left hand side first and solve it,
6(2+3) = 6(5) = 30,
Step3: Now consider right hand side first and solve it,
6(2) + 6(3) = 12 + 18 = 30.
From above example it is clear that L.H.S = R.H.S.
In this way we can use the distributive property to solve the arithmetic and algebraic Functions.

Using distributive property solve the equation x (5-y) and the value of x, y is 1, 2?

When we solve any equation by using distributive property then product and sum of number is equal to individual sum of product that is,
 m (n + o)= m(n)+m(o),
m (n + o)= mn + mo.
This property is very useful with mental Math. Now we can solve the given equation by using distributive property,
Step1: x (5 - y) = 5x - xy, in this example we use same property but difference is that we use negative sign instead of positive and then solve.
Step2: Let us consider left hand side first and solve it for x=1, y=2,
x(5-y)=1(5-2)=3,
Step3: Now consider right hand side first,
5x - xy = 5(1) – 2 = 3.
From above example it is clear that L.H.S = R.H.S. In this way we can use the distributive property to solve the arithmetic and algebraic Functions.

Solve (x + 3)(y + 7) by using distributive property for x = 3, y = 4?

When we solve any equation by using distributive property then product and sum of number is equal to individual sum of product that is,
 m (n + o)= m(n) + m(o),
m (n + o) = mn + mo.
This property is very useful with mental Math. Now we can solve the given equation by using distributive property,
Step1: (x + 3)(y + 7) = x(y) + x(7) + 3(y) + 3(7),
Step2: Let us consider left hand side first and solve it for x=3,y=4,
(x + 3)(y + 7) = (3 + 3)(4 + 7)=6 x 11 = 66.
Step3: Now consider right hand side first and solve it,
x(y) + x(7) + 3(y) + 3(7) = 3(4) + 3(7) + 3(4) + 3(7) = 66.
From above example it is clear that L.H.S = R.H.S.
In this way we can use the distributive property to solve the arithmetic and algebraic Functions.

Using distributive property solve the equation (3 + 5)(1 + 2)?

When we solve any equation by using distributive property then product and sum of number is equal to individual sum of product that is,
m (n + o) = m (n) + m(o),
m (n + o) = mn + mo.
This property is very useful with mental Math. Now we can solve the given equation by using distributive property,
Step1: (3 + 5)(1 + 2)=3(1) + 3(2) + 5(1) + 5(2),
Step2: Let us consider left hand side first and solve it,
(3 + 5)(1 + 2) = 8 x 3 = 24,
Step3: Now consider right hand side first and solve it,
3(1) + 3(2) + 5(1) + 5(2) = 3 + 6 + 5 + 10 = 24.
From above example it is clear that L.H.S = R.H.S.
In this way we can use the distributive property to solve the arithmetic and algebraic Functions.

Using distributive property solve the equation 7 (5 + 1)?

When we solve any equation by using distributive property then product and sum of number is equals to individual sum of product that is,
 m (n + o) = m(n) + m(o),
m (n + o)= mn + mo.
This property is very useful with mental Math. Now we can solve the given equation by using distributive property,
Step1: 7 (5 + 1) = 7(5) + 7(1),
Step2: Let us consider left hand side first and solve it,
7 (5 + 1) = 7 (6) = 42,
Step3: Now consider right hand side first and solve it,
7(5) + 7(1) = 35 + 7 = 42.
From above example it is clear that L.H.S = R.H.S. In this way we can use the distributive property to solve the arithmetic and algebraic Functions.

Solve (2 + x)(9 + y) by using distributive property for x = 1, y = 3?

When we solve any equation by using distributive property then product and sum of number is equals to individual sum of product that is,
 m (n + o) = m(n) + m(o),
m (n + o) = mn + mo.
This property is very useful with mental Math. Now we can solve the given equation by using distributive property,
Step1: (2 + x)(9 + y) = 2(9) + 2(y) + x(9) + x(y),
Step2: Let us consider left hand side first and solve it for x=1, y=3,
(2 + x)(9 + y) = (2 + 1)(9 + 3) = 3 x 12 = 36.
Step3: Now consider right hand side first and solve it,
2(9) + 2(y) + x(9) + x(y) = 2(9) + 2(3) + 1(9) + 1(3) = 18 + 6 + 9 + 3 = 36.
From above example it is clear that L.H.S = R.H.S. In this way we can use the distributive property to solve the arithmetic and algebraic Functions.

Using distributive property solve the equation 5(x + 2y) and the value of x, y is 2, 4?

When we solve any equation by using distributive property then product and sum of number is equals to individual sum of product that is,
 m (n + o) = m(n) + m(o),
m (n + o) = mn + mo.
This property is very useful with mental Math. Now we can solve the given equation by using distributive property,
Step1: 5 (x + 2y) = 5x + 10y, in this example we use same property but difference is that we use negative sign instead of positive and then solve.
Step2: Let us consider left hand side first and solve it for x=2, y=4,
5 (x + 2y) = 5(2 + 6) = 40,
Step3: Now consider right hand side first,
5x + 10y = 5(2) + 10(4) = 40.
From above example it is clear that L.H.S = R.H.S. In this way we can use the distributive property to solve the arithmetic and algebraic Functions.

Using distributive property solve the equation (10 - 5)(11 - 1)?

When we solve any equation by using distributive property then product and sum of number is equals to individual sum of product that is,
 m (n + o) = m(n) + m(o),
m(n + o)= mn + mo.
This property is very useful with mental Math. Now we can solve the given equation by using distributive property,
Step1: (10 - 5)(11 - 1) = 10(11) - 10(1) - 5(11) - 5(-1),
Step2: Let us consider left hand side first and solve it,
(10 - 5)(11 - 1) = 5 x 10 = 50,
Step3: Now consider right hand side first and solve it,
10(11) - 10(1) - 5(11) - 5(-1) = 110 – 10 – 55 + 5 = 50.
From above example it is clear that L.H.S = R.H.S. In this way we can use the distributive property to solve the arithmetic and algebraic Functions.

Using distributive property solve the equation 12(6 + 8)?

When we solve any equation by using distributive property then product and sum of number is equals to individual sum of product that is,
m (n + o) = m(n) + m(o),
m(n + o)= mn + mo.
This property is very useful with mental Math. Now we can solve the given equation by using distributive property,
Step1: 12 (6 + 8) = 12(6) + 12(8),
Step2: Let us consider left hand side first and solve it,
12(6 + 8) = 12(14) = 168,
Step3: Now consider right hand side first and solve it,
12(6) + 12(8) = 72 + 96 = 168.
From above example it is clear that L.H.S = R.H.S. In this way we can use the distributive property to solve the arithmetic and algebraic Functions.

Further Read

FAQ of Distributive Properties
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