Question

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

Answer 1

Answer:

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

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

(c) $\frac{1}{2}(x - 6) = \frac{1}{2}x - 3$

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

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

Step-by-step 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

$\frac{1}{2}(x - 6)$

Required

Express as a sum/difference

Apply distributive property

$\frac{1}{2}(x - 6) = \frac{1}{2}x - \frac{1}{2}*6$

$\frac{1}{2}(x - 6) = \frac{1}{2}x - \frac{6}{2}$

$\frac{1}{2}(x - 6) = \frac{1}{2}x - 3$

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:

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