The expression (3x-8)(2x+5) - (x+1)(2x+5) can be written as the product of 2x + 5 with what other binomial?

Question

I am currently confused on how to solve this equation. May I have assistance please?

Answer 1

Expand the whole expression out first.

 

(6x² - x - 40) - (2x² + 7x + 5) =

 

4x² - 8x - 45

 

 

Now we factor this expansion, using (2x + 5) as a starting point.

 

(2x + 5)( ____ ) = 4x² - 8x - 45

 

 

What binomial factor goes in the blank?

Answer 2

Johnson, just like 2a + 2a = 4a, 2(a + b) + 2(a + b) = 4(a + b).

 

In this case, (3x - 8)(2x + 5) - (x + 1)(2x + 5) = (3x - 8 - x - 1)(2x + 5) = (4x - 9)(2x + 5).

 

Your answer is 4x - 9.

Answer 3

Note you can factor out (2x+5):

 

(3x-8)(2x+5) - (x+1)(2x+5) = (2x+5)[(3x-8) - (x+1)]

 

Now simplify the expression (3x-8) - (x+1) in the bracket, and that will be the binomial that you seek.  Can you finish from here?

 

Answer 4

(3x-8)(2x+5)-(x+1)(2x+5)

factor out (2x+5)

(2x+5)([3x-8]-[x+1])

(2x+5)(3x-8-x-1)

(2x+5)(2x-9)