Factor by Grouping. PLEASE SHOW ME THE STEPS!

1.) 6x2-21xy+8xz-28yz
just to make it clear,the 2 infront of -21
is actualli an Exponent 2.

2.) x2+5x+7x+35

from now on, please use the notation 6x^2 to show 6x2.

both of your question are ideally set up for 'grouping'

6x2-21xy+8xz-28yz , I will factor the first two and then the last two
= 3x(2x - 7y) + 4z(2x - 7y)
now the 2x-7y is the common factor

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

(by expanding our answer we can see that it is correct if we get the original question back, we do!)

now you do the second one, and let me know how you did.

Sure! I'd be happy to help you with factoring by grouping. Here are the steps for each of the given expressions:

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

Step 1: Look for common factors among the terms. In this case, we can find a common factor of 3 from the first two terms and a common factor of 4 from the last two terms:

3(2x^2 - 7xy) + 4(2xz - 7yz)

Step 2: Next, factor out the common terms from each group. In the first group, we can factor out 2x:

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

Step 3: As you can see, we now have a common binomial factor of (x - 7y) in each group. Factor it out:

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

And the factored form of the expression is: (2x - 7y)(3x - 7y + 8z).

2.) x^2 + 5x + 7x + 35

Step 1: Regroup the terms so that you have two pairs that have a common factor. In this case, we can group the first two terms together and the last two terms together:

(x^2 + 5x) + (7x + 35)

Step 2: Look for common factors in each group. From the first group, we can factor out an x. From the second group, we can factor out 7:

x(x + 5) + 7(x + 5)

Step 3: Now, notice that both groups have a common binomial factor of (x + 5). Factor it out:

(x + 5)(x + 7)

So, the factored form of the expression is (x + 5)(x + 7).

I hope this helps! Let me know if you have any further questions.