describe and correct the error

Question

(3x-2)(2x-3)

=3x(2x-3)-2(2x-3)

=6x²-13x-6

Answer 1

When you expanded the product of two binomials by putting the greatest common factor in each term of the polynomial, you should distribute to get rid of parentheses.  Then combine like terms.  This way, you can avoid any mistakes and ensure that your result is correct.

 

 

3x(2x - 3) - 2(2x - 3)

 

 

Distribute.

 

6x² - 9x - 4x + 6

 

 

Combine like terms.

 

6x² + 13x + 6

Answer 2

The error is in the constant term.

 

The constant term in the result (-6) comes from the second term in the second line, which is:  -2(2x-3)

 

That should come out to -4x + 6, NOT -4x - 6 -- because -2 * -3 = 6

 

So the result should be 6x² - 13x + 6