SOLUTION: product for (3y^2+1)(3y^2-1)

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Question 106487: product for
(3y^2+1)(3y^2-1)
Answer by MathLover1(20849) About Me  (Show Source):
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Solved by pluggable solver: SIMPLIFY any expression (no substitution)
Your Result:


YOUR ANSWER


  • Graphical form: %283y%5E2%2B1%29%2A%283y%5E2-1%29 simplifies to 9%2Ay%5E%284%29-1
  • Text form: (3y^2+1)*(3y^2-1) simplifies to 9*y^(4)-1
  • Cartoon (animation) form: simplify_cartoon%28+%283y%5E2%2B1%29%2A%283y%5E2-1%29+%29
    For tutors: simplify_cartoon( (3y^2+1)*(3y^2-1) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%283%2Ay%5E2%2B1%29%2A%283%2Ay%5E2-1%29+%29.
Expanded term %283%2Ay%5E2-1%29 by using associative property on %283%2Ay%5E2%2B1%29
It becomes .
Look at %283%2Ay%5E2-1%29%2A3%2Ay%5E2%2B%283%2Ay%5E2-1%29%2Ahighlight_red%28+1+%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %283%2Ay%5E2-1%29%2A3%2Ay%5E2%2B%283%2Ay%5E2-1%29.
Look at %283%2Ay%5E2-1%29%2A3%2Ay%5E2%2Bhighlight_red%28+%283%2Ay%5E2-1%29+%29.
Remove unneeded parentheses around terms highlight_red%28+3%2Ay%5E2+%29,highlight_red%28+-1+%29
It becomes %283%2Ay%5E2-1%29%2A3%2Ay%5E2%2Bhighlight_green%28+3%2Ay%5E2+%29-highlight_green%28+1+%29.
Look at highlight_red%28+%283%2Ay%5E2-1%29%2A3%2Ay%5E2+%29%2B3%2Ay%5E2-1.
Expanded term 3%2Ay%5E2 by using associative property on %283%2Ay%5E2-1%29
It becomes .
Look at highlight_red%28+3+%29%2Ay%5E2%2Ahighlight_red%28+3+%29%2Ay%5E2-3%2Ay%5E2%2A1%2B3%2Ay%5E2-1.
Multiplied numerator integers
It becomes highlight_green%28+9+%29%2Ay%5E2%2Ay%5E2-3%2Ay%5E2%2A1%2B3%2Ay%5E2-1.
Look at 9%2Ay%5E2%2Ay%5E2-highlight_red%28+3+%29%2Ay%5E2%2Ahighlight_red%28+1+%29%2B3%2Ay%5E2-1.
Multiplied numerator integers
It becomes 9%2Ay%5E2%2Ay%5E2-highlight_green%28+3+%29%2Ay%5E2%2B3%2Ay%5E2-1.
Look at 9%2Ahighlight_red%28+y%5E2+%29%2Ahighlight_red%28+y%5E2+%29-3%2Ay%5E2%2B3%2Ay%5E2-1.
Reduce similar several occurrences of highlight_red%28+y%5E2+%29 to highlight_green%28+y%5E%282%2B2%29+%29
It becomes 9%2Ahighlight_green%28+y%5E%282%2B2%29+%29-3%2Ay%5E2%2B3%2Ay%5E2-1.
Look at 9%2Ay%5E%28highlight_red%28+2+%29%2Bhighlight_red%28+2+%29%29-3%2Ay%5E2%2B3%2Ay%5E2-1.
Added fractions or integers together
It becomes 9%2Ay%5E%28highlight_green%28+4+%29%29-3%2Ay%5E2%2B3%2Ay%5E2-1.
Look at 9%2Ay%5E%284%29-highlight_red%28+3%2Ay%5E2+%29%2Bhighlight_red%28+3%2Ay%5E2+%29-1.
Eliminated similar terms highlight_red%28+-3%2Ay%5E2+%29,highlight_red%28+3%2Ay%5E2+%29 replacing them with highlight_green%28+%28-3%2B3%29%2Ay%5E2+%29
It becomes 9%2Ay%5E%284%29%2Bhighlight_green%28+%28-3%2B3%29%2Ay%5E2+%29-1.
Look at 9%2Ay%5E%284%29%2Bhighlight_red%28+%28-3%2B3%29%2Ay%5E2+%29-1.
Since highlight_red%28+%28-3%2B3%29%2Ay%5E2+%29 has zero as a factor, it should be replaced with a zero
Look at 9%2Ay%5E%284%29%2B0-1.
Added fractions or integers together
It becomes 9%2Ay%5E%284%29%2B0-1.
Look at 9%2Ay%5E%284%29%2Bhighlight_red%28+0+%29-1.
Remove extraneous zero highlight_red%28+0+%29
It becomes 9%2Ay%5E%284%29-1.
Result: 9%2Ay%5E%284%29-1

Universal Simplifier and Solver


Done!