SOLUTION: (2x+6) (3x-7)=

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Question 36877This question is from textbook Introductory Algebra for College Students
: (2x+6) (3x-7)= This question is from textbook Introductory Algebra for College Students

Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
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YOUR ANSWER


  • Graphical form: %282x%2B6%29%2A%283x-7%29 simplifies to 6%2Ax%5E2%2B4%2Ax-42
  • Text form: (2x+6)*(3x-7) simplifies to 6*x^2+4*x-42
  • Cartoon (animation) form: simplify_cartoon%28+%282x%2B6%29%2A%283x-7%29+%29
    For tutors: simplify_cartoon( (2x+6)*(3x-7) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%282%2Ax%2B6%29%2A%283%2Ax-7%29+%29.
Expanded term %283%2Ax-7%29 by using associative property on %282%2Ax%2B6%29
It becomes highlight_green%28+%283%2Ax-7%29%2A2%2Ax+%29%2Bhighlight_green%28+%283%2Ax-7%29%2A6+%29.
Look at highlight_red%28+%283%2Ax-7%29%2A2%2Ax+%29%2B%283%2Ax-7%29%2A6.
Expanded term 2%2Ax by using associative property on %283%2Ax-7%29
It becomes highlight_green%28+2%2Ax%2A3%2Ax+%29-highlight_green%28+2%2Ax%2A7+%29%2B%283%2Ax-7%29%2A6.
Look at highlight_red%28+2+%29%2Ax%2Ahighlight_red%28+3+%29%2Ax-2%2Ax%2A7%2B%283%2Ax-7%29%2A6.
Multiplied numerator integers
It becomes highlight_green%28+6+%29%2Ax%2Ax-2%2Ax%2A7%2B%283%2Ax-7%29%2A6.
Look at 6%2Ax%2Ax-highlight_red%28+2+%29%2Ax%2Ahighlight_red%28+7+%29%2B%283%2Ax-7%29%2A6.
Multiplied numerator integers
It becomes 6%2Ax%2Ax-highlight_green%28+14+%29%2Ax%2B%283%2Ax-7%29%2A6.
Look at 6%2Ahighlight_red%28+x+%29%2Ahighlight_red%28+x+%29-14%2Ax%2B%283%2Ax-7%29%2A6.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes 6%2Ahighlight_green%28+x%5E2+%29-14%2Ax%2B%283%2Ax-7%29%2A6.
Look at 6%2Ax%5E2-14%2Ax%2Bhighlight_red%28+%283%2Ax-7%29%2A6+%29.
Expanded term 6 by using associative property on %283%2Ax-7%29
It becomes 6%2Ax%5E2-14%2Ax%2Bhighlight_green%28+6%2A3%2Ax+%29-highlight_green%28+6%2A7+%29.
Look at 6%2Ax%5E2-14%2Ax%2Bhighlight_red%28+6+%29%2Ahighlight_red%28+3+%29%2Ax-6%2A7.
Multiplied numerator integers
It becomes 6%2Ax%5E2-14%2Ax%2Bhighlight_green%28+18+%29%2Ax-6%2A7.
Look at 6%2Ax%5E2-14%2Ax%2B18%2Ax-highlight_red%28+6+%29%2Ahighlight_red%28+7+%29.
Multiplied numerator integers
It becomes 6%2Ax%5E2-14%2Ax%2B18%2Ax-highlight_green%28+42+%29.
Look at 6%2Ax%5E2-highlight_red%28+14%2Ax+%29%2Bhighlight_red%28+18%2Ax+%29-42.
Eliminated similar terms highlight_red%28+-14%2Ax+%29,highlight_red%28+18%2Ax+%29 replacing them with highlight_green%28+%28-14%2B18%29%2Ax+%29
It becomes 6%2Ax%5E2%2Bhighlight_green%28+%28-14%2B18%29%2Ax+%29-42.
Look at 6%2Ax%5E2%2B%28-highlight_red%28+14+%29%2Bhighlight_red%28+18+%29%29%2Ax-42.
Added fractions or integers together
It becomes 6%2Ax%5E2%2B%28highlight_green%28+4+%29%29%2Ax-42.
Look at 6%2Ax%5E2%2Bhighlight_red%28+%28highlight_red%28+4+%29%29%2Ax+%29-42.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes 6%2Ax%5E2%2Bhighlight_green%28+4+%29%2Ax-42.
Result: 6%2Ax%5E2%2B4%2Ax-42

Universal Simplifier and Solver


Done!

Hope this helps!