"abcdefghijklmnpqrstuvwxyz" randRange( 0, LETTERS.length - 2 ) LETTERS[ LETTER + 0 ] LETTERS[ LETTER + 1 ] function( a, b ) { return "(" + plus( a, b ) + ")"; }
randRangeNonZero( -10, 10 ) randRangeNonZero( -10, 10 ) randRangeNonZero( -1, 1 )

plus( A+PLUSPARENS( X, YSIGN+Y ), B )

Use the distributive property to simplify the expression.

plus( A+X, A*YSIGN+Y, B )

  • plus( A+X, YSIGN+Y, B )
  • plus( A+X, YSIGN+Y, A*B )
  • plus( A, X, YSIGN+Y, B )
  • plus( A+X, A+Y, fraction( B, A, true, true ) )
  • plus( fraction( 1, A, true, true )+X, fraction( YSIGN, A, true, true )+Y, B )
  • plus( A+X, A*YSIGN+Y, A+B )
  • plus( X, YSIGN+Y, A+B )
  • plus( X, YSIGN+Y, A*B )

Distribute across the parenthesis.

plus( A+PLUSPARENS( color( X, false ), color( YSIGN+Y, false ) ), B )

A negative sign before an expression is the same as -1 times that expression.

\color{ blue }{ -1 }*plus( PLUSPARENS( color( X, false ), color( YSIGN+Y, false ) ), B )

color( A, true )*color( X, false ) + color( A*YSIGN, true )*color( Y, false ) + B

plus( A+X, A*YSIGN+Y, B )

You're done!

Remember that the distributive property shows that multiplying an expression involving addition (or subtraction) by x is the same thing as multiplying each term of the expression by x before performing the addition.

x(y + z) = xy + xz

randRangeNonZero( -10, 10 ) randRangeNonZero( -1, 1 ) randRangeNonZero( -10, 10 ) randRangeNonZero( -10, 10 )

A + plus( B+PLUSPARENS( X, C ) ) + D

Using the distributive property, simplify the expression as much as possible.

plus( B+X, A+(B*C)+D )

  • X - A+(-1*C)+D
  • plus( B+X ) + A+C+D
  • X + A+(-1*C)+D
  • X - A+C+D
  • X + A+C+D
  • plus( A, B+X, C+D )
  • plus( A, B+X, (-1*C)+D )

The first and last numbers here can be combined to simplify the expression.

color( A, true ) + plus( B+PLUSPARENS( X, C ) ) + color( D, true )

plus( B+PLUSPARENS( X, C ) ) + color( A+D, true )

A negative sign before an expression is the same as -1 times that expression.

\color{ blue }{ -1 }*color( PLUSPARENS( X, C ), false ) + A+D

\color{ blue }{ -1*X + -1*C } + A+D

plus( B+X, B*C ) + A+D

plus( X, C, A+D )

plus( B+X, (B*C)+A+D )

You're done!

Remember that the distributive property shows that multiplying an expression involving addition (or subtraction) by x is the same thing as multiplying each term of the expression by x before performing the addition.

x(y + z) = xy + xz

randRangeNonZero( -10, 10 ) randRangeNonZero( -10, 10 ) randRangeNonZero( -10, 10 ) randRangeNonZero( -10, 10 )

plus( A+PLUSPARENS( X, B ), C+PLUSPARENS( D, X ) )

Using the distributive property, simplify the expression as much as possible.

plus( (A+C)+X, (A*B)+(C*D) )

  • plus( (A+1)+X, B+(C*D) )
  • plus( 2+X, A+B+C+D )
  • plus( (B+D)+X, A+C )
  • plus( A+PLUSPARENS( X, B ), C*D, C+X )
  • plus( (A+C)+X, B+(C*D) )
  • plus( (C+1)+X, A*B+C*D )
  • plus( A+X, A*B, C+PLUSPARENS( D, X ) )

Distribute across the first parenthesis.

plus( color( A, true )+color( PLUSPARENS( X, B ), false ), C+PLUSPARENS( D, X ) )

A negative sign before an expression is the same as -1 times that expression.

\color{ blue }{ -1 }*plus( color( PLUSPARENS( X, B ), false ), C+PLUSPARENS( D, X ) )

color( plus( A+X, A*B ), false ) + plus( C+PLUSPARENS( D, X ) )

Distribute across the second parenthesis.

plus( A+X, A*B ) + plus( color( C, true )+color( PLUSPARENS( D, X ), false ) )

A negative sign before an expression is the same as -1 times that expression.

plus( A+X, A*B ) + \color{ blue }{ -1 }*plus( color( PLUSPARENS( D, X ), false ) )

plus( A+X, A*B ) + color( plus( C*D, C+X ) )

Combine like terms.

color( A+X, true ) + color( A*B, false ) + color( C*D, false ) + color( C+X, true )

color( plus( (A+C)+X ), true ) + color( (A*B)+(C*D), false )

plus( (A+C)+X, (A*B)+(C*D) )

You're done! Make sure you simplify as much as possible.

Remember that the distributive property shows that multiplying an expression involving addition (or subtraction) by x is the same thing as multiplying each term of the expression by x before performing the addition.

x(y + z) = xy + xz

randRangeNonZero( -10, 10 ) randRangeNonZero( -10, 10 ) randRangeNonZero( -10, 10 )

plus( A+PLUSPARENS( X, B ), C+X )

Using the distributive property, simplify the expression as much as possible.

plus( (A+C)+X, A*B )

  • plus( (A+1)+X, B+C )
  • plus( 2+X, A+B+C )
  • plus( (A+C)+X, (-1*A*B) )
  • plus( ((-1*A)+C)+X, A*B )
  • plus( ((-1*A)+C)+X, (-1*A*B) )
  • plus( (A+C)+X, B )
  • plus( (1 + C)+X, A*B )

Distribute across the parenthesis.

\color{ blue }{ plus( A+PLUSPARENS( X, B ) ) } + plus( C+X )

A negative sign before an expression is the same as -1 times that expression.

\color{ blue }{ -1 }*plus( color( PLUSPARENS( X, B ), false ), plus( C+X ) )

color( plus( A+X, A*B ), false ) + plus( C+X )

Combine like terms.

color( A+X, true ) + color( A*B, false ) + color( C+X, true )

plus( (A+C)+X, A*B )

You're done!

Remember that the distributive property shows that multiplying an expression involving addition (or subtraction) by x is the same thing as multiplying each term of the expression by x before performing the addition.

x(y + z) = xy + xz