How do you simplify the product (6x - 5)(3x + 1)(6x5)(3x+1) and write it in standard form?

2 Answers
Jun 3, 2018

18x^2-9x-518x29x5

Explanation:

"each term in the second bracket is multiplied by each"each term in the second bracket is multiplied by each
"term in the first bracket"term in the first bracket

=(color(red)(6x-5))(3x+1)=(6x5)(3x+1)

=color(red)(6x)(3x+1)color(red)(-5)(3x+1)larrcolor(blue)"distribute"=6x(3x+1)5(3x+1)distribute

=(color(red)(6x)xx3x)+(color(red)(6x)xx1)+(color(red)(-5)xx3x)+(color(red)(-5)xx1)=(6x×3x)+(6x×1)+(5×3x)+(5×1)

=18x^2color(blue)(+6x)color(blue)(-15x)-5larrcolor(blue)"collect like terms"=18x2+6x15x5collect like terms

=18x^2-9x-5larrcolor(magenta)"in standard form"=18x29x5in standard form

Try using the FOIL method (First, Outside, Inside, Last)
18x^2-9x-518x29x5

Explanation:

You have to multiply each term in the left bracket by each term in the right bracket. The easiest way to make sure you don't miss anything is to use a systematic method such as FOIL.
The FOIL method means selecting those pairs of numbers to multiply together
Eg. (a+b)(c+d)=ac+ad+bc+bd(a+b)(c+d)=ac+ad+bc+bd

Question (6x-5)(3x+1)(6x5)(3x+1)
First: 6x*3x=18x^26x3x=18x2
Outside: 6x*1=6x6x1=6x
Inside:-5*3x=-15x53x=15x
Last: -5*1=-551=5
Now we add them together
(6x-5)(3x+1)=18x^2+6x+(-15x)+(-5)(6x5)(3x+1)=18x2+6x+(15x)+(5)
6x6x and -15x15x are like terms so they simplify
leaving us with
(6x-5)(3x+1)=18x^2-9x-5(6x5)(3x+1)=18x29x5