SOLUTION: simplify the following algebraic expression Multiply: (3x + 4) (3x -4)

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Question 35094: simplify the following algebraic expression
Multiply: (3x + 4) (3x -4)
Found 2 solutions by lyra, stanbon:
Answer by lyra(94) About Me  (Show Source):
You can put this solution on YOUR website!
%283x+%2B+4%29+%283x+-4%29
9x%5E2%2B12x-12x-16
9x%5E2-16
Also see:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %283x%2B4%29%2A%283x-4%29 simplifies to 9%2Ax%5E2-16
  • Text form: (3x+4)*(3x-4) simplifies to 9*x^2-16
  • Cartoon (animation) form: simplify_cartoon%28+%283x%2B4%29%2A%283x-4%29+%29
    For tutors: simplify_cartoon( (3x+4)*(3x-4) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%283%2Ax%2B4%29%2A%283%2Ax-4%29+%29.
Expanded term %283%2Ax-4%29 by using associative property on %283%2Ax%2B4%29
It becomes highlight_green%28+%283%2Ax-4%29%2A3%2Ax+%29%2Bhighlight_green%28+%283%2Ax-4%29%2A4+%29.
Look at highlight_red%28+%283%2Ax-4%29%2A3%2Ax+%29%2B%283%2Ax-4%29%2A4.
Expanded term 3%2Ax by using associative property on %283%2Ax-4%29
It becomes highlight_green%28+3%2Ax%2A3%2Ax+%29-highlight_green%28+3%2Ax%2A4+%29%2B%283%2Ax-4%29%2A4.
Look at highlight_red%28+3+%29%2Ax%2Ahighlight_red%28+3+%29%2Ax-3%2Ax%2A4%2B%283%2Ax-4%29%2A4.
Multiplied numerator integers
It becomes highlight_green%28+9+%29%2Ax%2Ax-3%2Ax%2A4%2B%283%2Ax-4%29%2A4.
Look at 9%2Ax%2Ax-highlight_red%28+3+%29%2Ax%2Ahighlight_red%28+4+%29%2B%283%2Ax-4%29%2A4.
Multiplied numerator integers
It becomes 9%2Ax%2Ax-highlight_green%28+12+%29%2Ax%2B%283%2Ax-4%29%2A4.
Look at 9%2Ahighlight_red%28+x+%29%2Ahighlight_red%28+x+%29-12%2Ax%2B%283%2Ax-4%29%2A4.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes 9%2Ahighlight_green%28+x%5E2+%29-12%2Ax%2B%283%2Ax-4%29%2A4.
Look at 9%2Ax%5E2-12%2Ax%2Bhighlight_red%28+%283%2Ax-4%29%2A4+%29.
Expanded term 4 by using associative property on %283%2Ax-4%29
It becomes 9%2Ax%5E2-12%2Ax%2Bhighlight_green%28+4%2A3%2Ax+%29-highlight_green%28+4%2A4+%29.
Look at 9%2Ax%5E2-12%2Ax%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+3+%29%2Ax-4%2A4.
Multiplied numerator integers
It becomes 9%2Ax%5E2-12%2Ax%2Bhighlight_green%28+12+%29%2Ax-4%2A4.
Look at 9%2Ax%5E2-12%2Ax%2B12%2Ax-highlight_red%28+4+%29%2Ahighlight_red%28+4+%29.
Multiplied numerator integers
It becomes 9%2Ax%5E2-12%2Ax%2B12%2Ax-highlight_green%28+16+%29.
Look at 9%2Ax%5E2-highlight_red%28+12%2Ax+%29%2Bhighlight_red%28+12%2Ax+%29-16.
Eliminated similar terms highlight_red%28+-12%2Ax+%29,highlight_red%28+12%2Ax+%29 replacing them with highlight_green%28+%28-12%2B12%29%2Ax+%29
It becomes 9%2Ax%5E2%2Bhighlight_green%28+%28-12%2B12%29%2Ax+%29-16.
Look at 9%2Ax%5E2%2Bhighlight_red%28+%28-12%2B12%29%2Ax+%29-16.
Since highlight_red%28+%28-12%2B12%29%2Ax+%29 has zero as a factor, it should be replaced with a zero
Look at 9%2Ax%5E2%2B0-16.
Added fractions or integers together
It becomes 9%2Ax%5E2%2B0-16.
Look at 9%2Ax%5E2%2Bhighlight_red%28+0+%29-16.
Remove extraneous zero highlight_red%28+0+%29
It becomes 9%2Ax%5E2-16.
Result: 9%2Ax%5E2-16

Universal Simplifier and Solver


Done!


Hope this helps,
lyra

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply: (3x + 4) (3x -4)
= (3x)^2 - (4)^2
=9x^2 - 4^2
=9x^2-16
Cheers,
Stan H.