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

Comments for Algebra - Distributive Property – Simplify Expressions

 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