SOLUTION: Expand (x-2)(x-5)(x+7)

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Question 21366: Expand (x-2)(x-5)(x+7)
Answer by Alwayscheerful(414) About Me  (Show Source):
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %28x-2%29%2A%28x-5%29%2A%28x%2B7%29 simplifies to x%5E%283%29-39%2Ax%2B70
  • Text form: (x-2)*(x-5)*(x+7) simplifies to x^(3)-39*x+70
  • Cartoon (animation) form: simplify_cartoon%28+%28x-2%29%2A%28x-5%29%2A%28x%2B7%29+%29
    For tutors: simplify_cartoon( (x-2)*(x-5)*(x+7) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28x-2%29%2A%28x-5%29%2A%28x%2B7%29+%29.
Expanded term %28x-5%29%2A%28x%2B7%29 by using associative property on %28x-2%29
It becomes .
Look at highlight_red%28+%28x-5%29%2A%28x%2B7%29%2Ax+%29-%28x-5%29%2A%28x%2B7%29%2A2.
Expanded term %28x%2B7%29%2Ax by using associative property on %28x-5%29
It becomes .
Look at .
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes %28x%2B7%29%2Ahighlight_green%28+x%5E2+%29-%28x%2B7%29%2Ax%2A5-%28x-5%29%2A%28x%2B7%29%2A2.
Look at highlight_red%28+%28x%2B7%29%2Ax%5E2+%29-%28x%2B7%29%2Ax%2A5-%28x-5%29%2A%28x%2B7%29%2A2.
Expanded term x%5E2 by using associative property on %28x%2B7%29
It becomes .
Look at .
Reduce similar several occurrences of highlight_red%28+x%5E2+%29 to highlight_green%28+x%5E%281%2B2%29+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at x%5E%283%29%2Bx%5E2%2A7-highlight_red%28+%28x%2B7%29%2Ax%2A5+%29-%28x-5%29%2A%28x%2B7%29%2A2.
Expanded term -x%2A5 by using associative property on %28x%2B7%29
It becomes .
Look at .
Multiplied numerator integers
It becomes x%5E%283%29%2Bx%5E2%2A7-x%2A5%2Ax-x%2Ahighlight_green%28+35+%29-%28x-5%29%2A%28x%2B7%29%2A2.
Look at .
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes x%5E%283%29%2Bx%5E2%2A7-highlight_green%28+x%5E2+%29%2A5-x%2A35-%28x-5%29%2A%28x%2B7%29%2A2.
Look at .
Eliminated similar terms highlight_red%28+x%5E2%2A7+%29,highlight_red%28+-x%5E2%2A5+%29 replacing them with highlight_green%28+%287-5%29%2Ax%5E2+%29
It becomes x%5E%283%29%2Bhighlight_green%28+%287-5%29%2Ax%5E2+%29-x%2A35-%28x-5%29%2A%28x%2B7%29%2A2.
Look at .
Added fractions or integers together
It becomes x%5E%283%29%2B%28highlight_green%28+2+%29%29%2Ax%5E2-x%2A35-%28x-5%29%2A%28x%2B7%29%2A2.
Look at .
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes x%5E%283%29%2Bhighlight_green%28+2+%29%2Ax%5E2-x%2A35-%28x-5%29%2A%28x%2B7%29%2A2.
Look at x%5E%283%29%2B2%2Ax%5E2-x%2A35-highlight_red%28+%28x-5%29%2A%28x%2B7%29%2A2+%29.
Expanded term -%28x%2B7%29%2A2 by using associative property on %28x-5%29
It becomes .
Look at .
Multiplied numerator integers
It becomes x%5E%283%29%2B2%2Ax%5E2-x%2A35-%28x%2B7%29%2A2%2Ax%2B%28x%2B7%29%2Ahighlight_green%28+10+%29.
Look at x%5E%283%29%2B2%2Ax%5E2-x%2A35-highlight_red%28+%28x%2B7%29%2A2%2Ax+%29%2B%28x%2B7%29%2A10.
Expanded term -2%2Ax by using associative property on %28x%2B7%29
It becomes .
Look at .
Multiplied numerator integers
It becomes x%5E%283%29%2B2%2Ax%5E2-x%2A35-2%2Ax%2Ax-highlight_green%28+14+%29%2Ax%2B%28x%2B7%29%2A10.
Look at .
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes x%5E%283%29%2B2%2Ax%5E2-x%2A35-2%2Ahighlight_green%28+x%5E2+%29-14%2Ax%2B%28x%2B7%29%2A10.
Look at .
Eliminated similar terms highlight_red%28+2%2Ax%5E2+%29,highlight_red%28+-2%2Ax%5E2+%29 replacing them with highlight_green%28+%282-2%29%2Ax%5E2+%29
It becomes x%5E%283%29%2Bhighlight_green%28+%282-2%29%2Ax%5E2+%29-x%2A35-14%2Ax%2B%28x%2B7%29%2A10.
Look at .
Eliminated similar terms highlight_red%28+-x%2A35+%29,highlight_red%28+-14%2Ax+%29 replacing them with highlight_green%28+%28-35-14%29%2Ax+%29
It becomes x%5E%283%29%2B%282-2%29%2Ax%5E2%2Bhighlight_green%28+%28-35-14%29%2Ax+%29%2B%28x%2B7%29%2A10.
Look at x%5E%283%29%2Bhighlight_red%28+%282-2%29%2Ax%5E2+%29%2B%28-35-14%29%2Ax%2B%28x%2B7%29%2A10.
Since highlight_red%28+%282-2%29%2Ax%5E2+%29 has zero as a factor, it should be replaced with a zero
Look at x%5E%283%29%2B0%2B%28-35-14%29%2Ax%2B%28x%2B7%29%2A10.
Added fractions or integers together
It becomes x%5E%283%29%2B0%2B%28-35-14%29%2Ax%2B%28x%2B7%29%2A10.
Look at .
Added fractions or integers together
It becomes x%5E%283%29%2B0%2B%28highlight_green%28+-49+%29%29%2Ax%2B%28x%2B7%29%2A10.
Look at x%5E%283%29%2Bhighlight_red%28+0+%29%2B%28-49%29%2Ax%2B%28x%2B7%29%2A10.
Remove extraneous zero highlight_red%28+0+%29
It becomes x%5E%283%29%2B%28-49%29%2Ax%2B%28x%2B7%29%2A10.
Look at x%5E%283%29%2B%28highlight_red%28+-49+%29%29%2Ax%2B%28x%2B7%29%2A10.
Removed extra sign in front of -49
It becomes x%5E%283%29%2B%28-highlight_green%28+49+%29%29%2Ax%2B%28x%2B7%29%2A10.
Look at x%5E%283%29%2Bhighlight_red%28+%28-highlight_red%28+49+%29%29%2Ax+%29%2B%28x%2B7%29%2A10.
Remove unneeded parentheses around factor highlight_red%28+49+%29
It becomes x%5E%283%29-highlight_green%28+49+%29%2Ax%2B%28x%2B7%29%2A10.
Look at x%5E%283%29-49%2Ax%2Bhighlight_red%28+%28x%2B7%29%2A10+%29.
Expanded term 10 by using associative property on %28x%2B7%29
It becomes x%5E%283%29-49%2Ax%2Bhighlight_green%28+10%2Ax+%29%2Bhighlight_green%28+10%2A7+%29.
Look at x%5E%283%29-49%2Ax%2B10%2Ax%2Bhighlight_red%28+10+%29%2Ahighlight_red%28+7+%29.
Multiplied numerator integers
It becomes x%5E%283%29-49%2Ax%2B10%2Ax%2Bhighlight_green%28+70+%29.
Look at x%5E%283%29-highlight_red%28+49%2Ax+%29%2Bhighlight_red%28+10%2Ax+%29%2B70.
Eliminated similar terms highlight_red%28+-49%2Ax+%29,highlight_red%28+10%2Ax+%29 replacing them with highlight_green%28+%28-49%2B10%29%2Ax+%29
It becomes x%5E%283%29%2Bhighlight_green%28+%28-49%2B10%29%2Ax+%29%2B70.
Look at x%5E%283%29%2B%28-highlight_red%28+49+%29%2Bhighlight_red%28+10+%29%29%2Ax%2B70.
Added fractions or integers together
It becomes x%5E%283%29%2B%28highlight_green%28+-39+%29%29%2Ax%2B70.
Look at x%5E%283%29%2B%28highlight_red%28+-39+%29%29%2Ax%2B70.
Removed extra sign in front of -39
It becomes x%5E%283%29%2B%28-highlight_green%28+39+%29%29%2Ax%2B70.
Look at x%5E%283%29%2Bhighlight_red%28+%28-highlight_red%28+39+%29%29%2Ax+%29%2B70.
Remove unneeded parentheses around factor highlight_red%28+39+%29
It becomes x%5E%283%29-highlight_green%28+39+%29%2Ax%2B70.
Result: x%5E%283%29-39%2Ax%2B70

Universal Simplifier and Solver


Done!

Hope this helps!