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Algebra - Distributive Property – Simplify Expressions











































Algebra – the Distributive Property

Use the Distributive Property to simplify each of the following expressions :

1. 30(x + 3)
2. 8(5 + 2x)
3. x(x + 2)
4. 3(x + z) + z(2 + x)
5. 4z + 6(7 + 3y)
6. 30(30 + y) + y
7. 0(x - 100)
8. y(5 + 2x)
9. 20(x + 7)
10. 1(xz + z) + z(2 + x)
11. 5x + x(7 + 3y)
12. 3(3 + y) + 3y

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Jun 25, 2012
Distributive Property
by: Staff


The answer:

The Distributive Property combines the following two operations in mathematics: multiplication and addition . It is formally defined as "the distribution of multiplication over addition".

It is used to simplify an expression containing parentheses to an expression without parentheses.


30(x + 3)

Multiply the sum of x and 3 by 30

= 30*x + 30*3

= 30x + 90



8(5 + 2x)

Multiply the sum of 5 and 2x by 8

= 8*5 + 8*(2x)

= 40 + 16x

= 16x + 40




x(x + 2)

Multiply the sum of x and 2 by x

= x*x + x*2

= x² + 2x



3(x + z) + z(2 + x)

Multiply the sum of x and z by 3, multiply the sum of 2 and x by z, and then add the two values

= 3*x + 3*z + z*2 + z*x

= 3x + 3z + 2z + xz

= 3x + 5z + xz



4z + 6(7 + 3y)

Multiply the sum of 7 and 3y by 6, and then add 4z

= 4z + 6*7 + 6*3y

= 4z + 42 + 18y

= 4z + 18y + 42



30(30 + y) + y

Multiply the sum of 30 and y by 30, and then add y

= 30*30 + 30*y +y

= 900 + 30y + y

= 900 + 31y

= 31y + 900



0(x - 100)

Multiply the sum of x and -100 by 0

Anything multiplied by 0 is 0

0(x - 100) = 0



y(5 + 2x)

Multiply the sum of 5 and 2x by y

= y*5 + 5*2x

= 5y + 10x



20(x + 7)

Multiply the sum of x and 7 by 20

= 20*x + 20*7

= 20x + 140



1(xz + z) + z(2 + x)

Multiply the sum of xz and z by 1, multiply the sum of 2 and x by z, and then add the two results

= 1*xz + 1*z + z*2 + z*x

= xz + z + 2z + xz

= 2xz + 3z



5x + x(7 + 3y)

Multiply the sum of 7 and 3y by x, and add that value to 5x

= 5x + x*7 + x*3y

= 5x + 7x + 3xy

= 12x + 3xy



3(3 + y) + 3y

Multiply the sum of 3 and y by 3, and add that value to 3y

= 3*3 + 3*y + 3y

= 9 + 3y + 3y

= 9 + 6y

= 6y + 9





Thanks for writing.

Staff
www.solving-math-problems.com


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