SOLUTION: did i solve this right? (4m-3n)(4m+3n) =4m*4m=16m^2 3n*3n=9n^2 =16m^2+n^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: did i solve this right? (4m-3n)(4m+3n) =4m*4m=16m^2 3n*3n=9n^2 =16m^2+n^2      Log On


   

Question 75553: did i solve this right?
(4m-3n)(4m+3n)
=4m*4m=16m^2
3n*3n=9n^2
=16m^2+n^2
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
Your Result:


YOUR ANSWER


  • Graphical form: %284m-3n%29%2A%284m%2B3n%29 simplifies to 16%2Am%5E2-9%2An%5E2
  • Text form: (4m-3n)*(4m+3n) simplifies to 16*m^2-9*n^2
  • Cartoon (animation) form: simplify_cartoon%28+%284m-3n%29%2A%284m%2B3n%29+%29
    For tutors: simplify_cartoon( (4m-3n)*(4m+3n) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%284%2Am-3%2An%29%2A%284%2Am%2B3%2An%29+%29.
Expanded term %284%2Am%2B3%2An%29 by using associative property on %284%2Am-3%2An%29
It becomes .
Look at highlight_red%28+%284%2Am%2B3%2An%29%2A4%2Am+%29-%284%2Am%2B3%2An%29%2A3%2An.
Expanded term 4%2Am by using associative property on %284%2Am%2B3%2An%29
It becomes .
Look at .
Multiplied numerator integers
It becomes highlight_green%28+16+%29%2Am%2Am%2B4%2Am%2A3%2An-%284%2Am%2B3%2An%29%2A3%2An.
Look at .
Multiplied numerator integers
It becomes 16%2Am%2Am%2Bhighlight_green%28+12+%29%2Am%2An-%284%2Am%2B3%2An%29%2A3%2An.
Look at .
Reduce similar several occurrences of highlight_red%28+m+%29 to highlight_green%28+m%5E2+%29
It becomes 16%2Ahighlight_green%28+m%5E2+%29%2B12%2Am%2An-%284%2Am%2B3%2An%29%2A3%2An.
Look at 16%2Am%5E2%2B12%2Am%2An-highlight_red%28+%284%2Am%2B3%2An%29%2A3%2An+%29.
Expanded term -3%2An by using associative property on %284%2Am%2B3%2An%29
It becomes .
Look at .
Multiplied numerator integers
It becomes 16%2Am%5E2%2B12%2Am%2An-highlight_green%28+12+%29%2An%2Am-3%2An%2A3%2An.
Look at 16%2Am%5E2%2B12%2Am%2An-12%2An%2Am-highlight_red%28+3+%29%2An%2Ahighlight_red%28+3+%29%2An.
Multiplied numerator integers
It becomes 16%2Am%5E2%2B12%2Am%2An-12%2An%2Am-highlight_green%28+9+%29%2An%2An.
Look at 16%2Am%5E2%2B12%2Am%2An-12%2An%2Am-9%2Ahighlight_red%28+n+%29%2Ahighlight_red%28+n+%29.
Reduce similar several occurrences of highlight_red%28+n+%29 to highlight_green%28+n%5E2+%29
It becomes 16%2Am%5E2%2B12%2Am%2An-12%2An%2Am-9%2Ahighlight_green%28+n%5E2+%29.
Look at 16%2Am%5E2%2Bhighlight_red%28+12%2Am%2An+%29-highlight_red%28+12%2An%2Am+%29-9%2An%5E2.
Eliminated similar terms highlight_red%28+12%2Am%2An+%29,highlight_red%28+-12%2An%2Am+%29 replacing them with highlight_green%28+%2812-12%29%2Am%2An+%29
It becomes 16%2Am%5E2%2Bhighlight_green%28+%2812-12%29%2Am%2An+%29-9%2An%5E2.
Look at 16%2Am%5E2%2Bhighlight_red%28+%2812-12%29%2Am%2An+%29-9%2An%5E2.
Since highlight_red%28+%2812-12%29%2Am%2An+%29 has zero as a factor, it should be replaced with a zero
Look at 16%2Am%5E2%2B0-9%2An%5E2.
Added fractions or integers together
It becomes 16%2Am%5E2%2B0-9%2An%5E2.
Look at 16%2Am%5E2%2Bhighlight_red%28+0+%29-9%2An%5E2.
Remove extraneous zero highlight_red%28+0+%29
It becomes 16%2Am%5E2-9%2An%5E2.
Result: 16%2Am%5E2-9%2An%5E2

Universal Simplifier and Solver


Done!

When two terms in parenthesis are adjacent to each other, you need to multiply them, not set them equal to each other.
Hope this helps!