SOLUTION: Add and simplify: (2/3x^2 - 14x + 16) + (1/3x^2 - 17x + 24)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Add and simplify: (2/3x^2 - 14x + 16) + (1/3x^2 - 17x + 24)      Log On


   

Question 387937: Add and simplify:
(2/3x^2 - 14x + 16) + (1/3x^2 - 17x + 24)
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Add, Subtract and Multiply Polynomials and Simplify
Your Result:


YOUR ANSWER


  • Graphical form: %282%2F3%2Ax%5E2-14%2Ax%2B16%29%2B%281%2F3%2Ax%5E2-17%2Ax%2B24%29 simplifies to x%5E2-31%2Ax%2B40
  • Text form: (2/3*x^2-14*x+16)+(1/3*x^2-17*x+24) simplifies to x^2-31*x+40
  • Cartoon (animation) form: simplify_cartoon%28+%282%2F3%2Ax%5E2-14%2Ax%2B16%29%2B%281%2F3%2Ax%5E2-17%2Ax%2B24%29+%29
    For tutors: simplify_cartoon( (2/3*x^2-14*x+16)+(1/3*x^2-17*x+24) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%282%2F3%2Ax%5E2-14%2Ax%2B16%29+%29%2B%281%2F3%2Ax%5E2-17%2Ax%2B24%29.
Remove unneeded parentheses around terms highlight_red%28+2%2F3%2Ax%5E2+%29,highlight_red%28+-14%2Ax+%29,highlight_red%28+16+%29
It becomes .
Look at 2%2F3%2Ax%5E2-14%2Ax%2B16%2Bhighlight_red%28+%281%2F3%2Ax%5E2-17%2Ax%2B24%29+%29.
Remove unneeded parentheses around terms highlight_red%28+1%2F3%2Ax%5E2+%29,highlight_red%28+-17%2Ax+%29,highlight_red%28+24+%29
It becomes .
Look at 2%2F3%2Ax%5E2-14%2Ax%2B16%2Bhighlight_red%28+1+%29%2F3%2Ax%5E2-17%2Ax%2B24.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes 2%2F3%2Ax%5E2-14%2Ax%2B16%2Bx%5E2%2F3-17%2Ax%2B24.
Look at 2%2F3%2Ax%5E2-14%2Ax%2Bhighlight_red%28+16+%29%2Bx%5E2%2F3-17%2Ax%2Bhighlight_red%28+24+%29.
Added fractions or integers together
It becomes 2%2F3%2Ax%5E2-14%2Ax%2Bhighlight_green%28+40+%29%2Bx%5E2%2F3-17%2Ax.
Look at 2%2F3%2Ax%5E2-14%2Ax%2Bhighlight_red%28+40+%29%2Bx%5E2%2F3-17%2Ax.
Moved 40 to the right of expression
It becomes 2%2F3%2Ax%5E2-14%2Ax%2Bx%5E2%2F3-17%2Ax%2Bhighlight_green%28+40+%29.
Look at highlight_red%28+2%2F3%2Ax%5E2+%29-14%2Ax%2Bhighlight_red%28+x%5E2%2F3+%29-17%2Ax%2B40.
Eliminated similar terms highlight_red%28+2%2F3%2Ax%5E2+%29,highlight_red%28+x%5E2%2F3+%29 replacing them with highlight_green%28+%282%2A1%2F3%2B1%2F3%29%2Ax%5E2+%29
It becomes highlight_green%28+%282%2A1%2F3%2B1%2F3%29%2Ax%5E2+%29-14%2Ax-17%2Ax%2B40.
Look at %282%2A1%2F3%2B1%2F3%29%2Ax%5E2-highlight_red%28+14%2Ax+%29-highlight_red%28+17%2Ax+%29%2B40.
Eliminated similar terms highlight_red%28+-14%2Ax+%29,highlight_red%28+-17%2Ax+%29 replacing them with highlight_green%28+%28-14-17%29%2Ax+%29
It becomes %282%2A1%2F3%2B1%2F3%29%2Ax%5E2%2Bhighlight_green%28+%28-14-17%29%2Ax+%29%2B40.
Look at highlight_red%28+%282%2A1%2F3%2B1%2F3%29+%29%2Ax%5E2%2B%28-14-17%29%2Ax%2B40.
Remove extraneous '1' from product highlight_red%28+%282%2A1%2F3%2B1%2F3%29+%29
It becomes x%5E2%2B%28-14-17%29%2Ax%2B40.
Look at x%5E2%2B%28-highlight_red%28+14+%29-highlight_red%28+17+%29%29%2Ax%2B40.
Added fractions or integers together
It becomes x%5E2%2B%28highlight_green%28+-31+%29%29%2Ax%2B40.
Look at x%5E2%2B%28highlight_red%28+-31+%29%29%2Ax%2B40.
Removed extra sign in front of -31
It becomes x%5E2%2B%28-highlight_green%28+31+%29%29%2Ax%2B40.
Look at x%5E2%2Bhighlight_red%28+%28-highlight_red%28+31+%29%29%2Ax+%29%2B40.
Remove unneeded parentheses around factor highlight_red%28+31+%29
It becomes x%5E2-highlight_green%28+31+%29%2Ax%2B40.
Result: x%5E2-31%2Ax%2B40

Universal Simplifier and Solver


Done!
x^2-31*x+40