SOLUTION: Can you help me solve this: Apply the distributive property. Then simplify by combining like terms: (2w+4)(-3)+w and {{{ 15d^2+(2-d)4d }}}?

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Can you help me solve this: Apply the distributive property. Then simplify by combining like terms: (2w+4)(-3)+w and {{{ 15d^2+(2-d)4d }}}?      Log On


   

Question 631435: Can you help me solve this: Apply the distributive property. Then simplify by combining like terms: (2w+4)(-3)+w and +15d%5E2%2B%282-d%294d+?
Answer by 55305(86) 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: %282w%2B4%29%2A%28-3%29%2Bw simplifies to -5%2Aw-12
  • Text form: (2w+4)*(-3)+w simplifies to -5*w-12
  • Cartoon (animation) form: simplify_cartoon%28+%282w%2B4%29%2A%28-3%29%2Bw+%29
    For tutors: simplify_cartoon( (2w+4)*(-3)+w )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%282%2Aw%2B4%29%2A%28-highlight_red%28+3+%29%29+%29%2Bw.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes -%282%2Aw%2B4%29%2Ahighlight_green%28+3+%29%2Bw.
Look at -highlight_red%28+%282%2Aw%2B4%29%2A3+%29%2Bw.
Expanded term -3 by using associative property on %282%2Aw%2B4%29
It becomes -highlight_green%28+3%2A2%2Aw+%29-highlight_green%28+3%2A4+%29%2Bw.
Look at -highlight_red%28+3+%29%2Ahighlight_red%28+2+%29%2Aw-3%2A4%2Bw.
Multiplied numerator integers
It becomes -highlight_green%28+6+%29%2Aw-3%2A4%2Bw.
Look at -6%2Aw-highlight_red%28+3+%29%2Ahighlight_red%28+4+%29%2Bw.
Multiplied numerator integers
It becomes -6%2Aw-highlight_green%28+12+%29%2Bw.
Look at -6%2Aw-highlight_red%28+12+%29%2Bw.
Moved -12 to the right of expression
It becomes -6%2Aw%2Bw-highlight_green%28+12+%29.
Look at -highlight_red%28+6%2Aw+%29%2Bhighlight_red%28+w+%29-12.
Eliminated similar terms highlight_red%28+-6%2Aw+%29,highlight_red%28+w+%29 replacing them with highlight_green%28+%28-6%2B1%29%2Aw+%29
It becomes highlight_green%28+%28-6%2B1%29%2Aw+%29-12.
Look at %28-highlight_red%28+6+%29%2Bhighlight_red%28+1+%29%29%2Aw-12.
Added fractions or integers together
It becomes %28highlight_green%28+-5+%29%29%2Aw-12.
Look at %28highlight_red%28+-5+%29%29%2Aw-12.
Removed extra sign in front of -5
It becomes %28-highlight_green%28+5+%29%29%2Aw-12.
Look at highlight_red%28+%28-highlight_red%28+5+%29%29%2Aw+%29-12.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes -highlight_green%28+5+%29%2Aw-12.
Result: -5%2Aw-12

Universal Simplifier and Solver


Done!

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: 15d%5E2%2B%282-d%29%2A4d simplifies to 11%2Ad%5E2%2B8%2Ad
  • Text form: 15d^2+(2-d)*4d simplifies to 11*d^2+8*d
  • Cartoon (animation) form: simplify_cartoon%28+15d%5E2%2B%282-d%29%2A4d+%29
    For tutors: simplify_cartoon( 15d^2+(2-d)*4d )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 15%2Ad%5E2%2B%28highlight_red%28+2+%29-d%29%2A4%2Ad.
Moved 2 to the right of expression
It becomes 15%2Ad%5E2%2B%28-d%2Bhighlight_green%28+2+%29%29%2A4%2Ad.
Look at 15%2Ad%5E2%2Bhighlight_red%28+%28-d%2B2%29%2A4%2Ad+%29.
Expanded term 4%2Ad by using associative property on %28-d%2B2%29
It becomes 15%2Ad%5E2-highlight_green%28+4%2Ad%2Ad+%29%2Bhighlight_green%28+4%2Ad%2A2+%29.
Look at 15%2Ad%5E2-4%2Ad%2Ad%2Bhighlight_red%28+4+%29%2Ad%2Ahighlight_red%28+2+%29.
Multiplied numerator integers
It becomes 15%2Ad%5E2-4%2Ad%2Ad%2Bhighlight_green%28+8+%29%2Ad.
Look at 15%2Ad%5E2-4%2Ahighlight_red%28+d+%29%2Ahighlight_red%28+d+%29%2B8%2Ad.
Reduce similar several occurrences of highlight_red%28+d+%29 to highlight_green%28+d%5E2+%29
It becomes 15%2Ad%5E2-4%2Ahighlight_green%28+d%5E2+%29%2B8%2Ad.
Look at highlight_red%28+15%2Ad%5E2+%29-highlight_red%28+4%2Ad%5E2+%29%2B8%2Ad.
Eliminated similar terms highlight_red%28+15%2Ad%5E2+%29,highlight_red%28+-4%2Ad%5E2+%29 replacing them with highlight_green%28+%2815-4%29%2Ad%5E2+%29
It becomes highlight_green%28+%2815-4%29%2Ad%5E2+%29%2B8%2Ad.
Look at %28highlight_red%28+15+%29-highlight_red%28+4+%29%29%2Ad%5E2%2B8%2Ad.
Added fractions or integers together
It becomes %28highlight_green%28+11+%29%29%2Ad%5E2%2B8%2Ad.
Look at highlight_red%28+%28highlight_red%28+11+%29%29%2Ad%5E2+%29%2B8%2Ad.
Remove unneeded parentheses around factor highlight_red%28+11+%29
It becomes highlight_green%28+11+%29%2Ad%5E2%2B8%2Ad.
Result: 11%2Ad%5E2%2B8%2Ad

Universal Simplifier and Solver


Done!