Answer:
(a) [tex]5 * (2x - 1) = 10x - 5[/tex]
(b) [tex]6 * x = x + 2x + 3x[/tex]
(c) [tex]\frac{1}{2}(x - 6) = \frac{1}{2}x - 3[/tex]
(d) [tex]y(3x + 4z) = 3xy + 4yz[/tex]
(e) [tex]z(2xy - 3y + 4x) = 2xyz - 3yz + 4xz[/tex]
Step-by-step explanation:
Solving (a):
Given
[tex]10x - 5[/tex]
Required
Express as a product
Express 10x as 5 * 2x
[tex]10x - 5 = 5 * 2x - 5[/tex]
Apply distributive property
[tex]10x - 5 = 5(2x - 1)[/tex]
[tex]10x - 5 = 5 * (2x - 1)[/tex]
So:
[tex]5 * (2x - 1) = 10x - 5[/tex]
Solving (b):
Given
[tex]x + 2x + 3x[/tex]
Required
Express as a product
Express 2x and 3x as 2 * x and 3 * x, respectively
[tex]x + 2x + 3x = x + 2*x + 3*x[/tex]
Apply distributive property
[tex]x + 2x + 3x = x(1 + 2 + 3)[/tex]
[tex]x + 2x + 3x = x(6)[/tex]
[tex]x + 2x + 3x = 6*x[/tex]
So:
[tex]6 * x = x + 2x + 3x[/tex]
Solving (c):
Given
[tex]\frac{1}{2}(x - 6)[/tex]
Required
Express as a sum/difference
Apply distributive property
[tex]\frac{1}{2}(x - 6) = \frac{1}{2}x - \frac{1}{2}*6[/tex]
[tex]\frac{1}{2}(x - 6) = \frac{1}{2}x - \frac{6}{2}[/tex]
[tex]\frac{1}{2}(x - 6) = \frac{1}{2}x - 3[/tex]
Solving (d):
Given
[tex]y(3x + 4z)[/tex]
Required
Express as a sum/difference
Apply distributive property
[tex]y(3x + 4z) = 3x * y + 4z * y[/tex]
[tex]y(3x + 4z) = 3xy + 4yz[/tex]
Solving (e):
Given
[tex]2xyz - 3yz + 4xz[/tex]
Required
Express as a product
Factorize
[tex]2xyz - 3yz + 4xz = 2xy * z - 3y * z + 4x * z[/tex]
Apply distributive property
[tex]2xyz - 3yz + 4xz = z(2xy - 3y + 4x)[/tex]
So:
[tex]z(2xy - 3y + 4x) = 2xyz - 3yz + 4xz[/tex]
