# Factor the algebraic expression 6x2 - 21xy + 8xz - 28yz.

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simplify:

Let E = 6x2 - 21xy + 8xz - 28yz

Let us group sides:

E = ( 6x^2 -21xy ) + (8xz - 28yz)

Factor 3x from the first 2 terms:

==> E = 3x(2x -7y) + (8xz- 28yz)

Now we will factor 4z from the second two terms:

==> E = 3x(2x-7y) + 4z(2x - 7y)

Now factor (2x-7y)

==> E = ( 2x-7y)( 3x + 4z)

Then the final simplified expression is:

**( 2x -7y) ( 3x + 4z)**

Given:-

6(x^2) - 21xy + 8xz - 28yz

or, 3x(2x - 7y) + 4z(2x - 7y)

or, (3x + 4z)*(2x - 7y)

We'll group the first 2 terms and the last 2 terms:

(6x^2 - 21xy) + (8xz - 28yz) (1)

We'll consider the first pair of brackets:

(6x^2 - 21xy)

We'll factorize by 3x:

(6x^2 - 21xy) = 3x(2x - 7y) (2)

We'll consider the 2nd pair of brackets:

(8xz - 28yz)

We'll factorize by 4z:

(8xz - 28yz) = 4z(2x - 7y) (3)

We'll substitute (2) and (3) in (1):

(6x^2 - 21xy) + (8xz - 28yz) = 3x(2x - 7y) + 4z(2x - 7y)

We'll factorize by (2x - 7y):

** (6x^2 - 21xy) + (8xz - 28yz) = (2x - 7y)(3x + 4z)**

6x2 - 21xy + 8xz - 28yz

(6x2 - 21xy ) + ( 8xz - 28yz )

3x ( 2x - 7y ) + 4z ( 2x - 7y)

(3x + 4z) (2x - 7y)

6x2 - 21xy + 8xz - 28yz

group:

(6x2 - 21xy ) + ( 8xz - 28yz )

Factor out the greatest common factors:

3x ( 2x - 7y ) + 4z ( 2x - 7y)

group the factors outside of the parentheses:

(3x + 4z) (2x - 7y)

and that's the answer