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Please help me! I'm stuck and really confused, thank you so much!

Please help me! I'm stuck and really confused, thank you so much!-example-1

1 Answer

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Answer:

(a)
5 * (2x - 1) = 10x - 5

(b)
6 * x = x + 2x + 3x

(c)
(1)/(2)(x - 6) = (1)/(2)x - 3

(d)
y(3x + 4z) = 3xy + 4yz

(e)
z(2xy - 3y + 4x) = 2xyz - 3yz + 4xz

Explanation:

Solving (a):

Given


10x - 5

Required

Express as a product

Express 10x as 5 * 2x


10x - 5 = 5 * 2x - 5

Apply distributive property


10x - 5 = 5(2x - 1)


10x - 5 = 5 * (2x - 1)

So:


5 * (2x - 1) = 10x - 5

Solving (b):

Given


x + 2x + 3x

Required

Express as a product

Express 2x and 3x as 2 * x and 3 * x, respectively


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

Apply distributive property


x + 2x + 3x = x(1 + 2 + 3)


x + 2x + 3x = x(6)


x + 2x + 3x = 6*x

So:


6 * x = x + 2x + 3x

Solving (c):

Given


(1)/(2)(x - 6)

Required

Express as a sum/difference

Apply distributive property


(1)/(2)(x - 6) = (1)/(2)x - (1)/(2)*6


(1)/(2)(x - 6) = (1)/(2)x - (6)/(2)


(1)/(2)(x - 6) = (1)/(2)x - 3

Solving (d):

Given


y(3x + 4z)

Required

Express as a sum/difference

Apply distributive property


y(3x + 4z) = 3x * y + 4z * y


y(3x + 4z) = 3xy + 4yz

Solving (e):

Given


2xyz - 3yz + 4xz

Required

Express as a product

Factorize


2xyz - 3yz + 4xz = 2xy * z - 3y * z + 4x * z

Apply distributive property


2xyz - 3yz + 4xz = z(2xy - 3y + 4x)

So:


z(2xy - 3y + 4x) = 2xyz - 3yz + 4xz

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