Question
Simplify the expression
−27p3q5r4−27p5q4r3+27p4q5r3−27p4q3r5+27p3q4r5+27p5q3r4
Evaluate
p3(q−r)×3q3(r−p)×3r3(p−q)×3
Rewrite the expression in exponential form
p3(q−r)×33q3(r−p)r3(p−q)
Multiply the terms
More Steps

Evaluate
p3×33q3r3
Use the commutative property to reorder the terms
33p3q3r3
Evaluate the power
27p3q3r3
27p3q3r3(q−r)(r−p)(p−q)
Multiply the terms
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Evaluate
27p3q3r3(q−r)
Apply the distributive property
27p3q3r3q−27p3q3r3×r
Multiply the terms
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Evaluate
q3×q
Use the product rule an×am=an+m to simplify the expression
q3+1
Add the numbers
q4
27p3q4r3−27p3q3r3×r
Multiply the terms
More Steps

Evaluate
r3×r
Use the product rule an×am=an+m to simplify the expression
r3+1
Add the numbers
r4
27p3q4r3−27p3q3r4
(27p3q4r3−27p3q3r4)(r−p)(p−q)
Multiply the terms
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Evaluate
(27p3q4r3−27p3q3r4)(r−p)
Apply the distributive property
27p3q4r3×r−27p3q4r3p−27p3q3r4×r−(−27p3q3r4p)
Multiply the terms
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Evaluate
r3×r
Use the product rule an×am=an+m to simplify the expression
r3+1
Add the numbers
r4
27p3q4r4−27p3q4r3p−27p3q3r4×r−(−27p3q3r4p)
Multiply the terms
More Steps

Evaluate
p3×p
Use the product rule an×am=an+m to simplify the expression
p3+1
Add the numbers
p4
27p3q4r4−27p4q4r3−27p3q3r4×r−(−27p3q3r4p)
Multiply the terms
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Evaluate
r4×r
Use the product rule an×am=an+m to simplify the expression
r4+1
Add the numbers
r5
27p3q4r4−27p4q4r3−27p3q3r5−(−27p3q3r4p)
Multiply the terms
More Steps

Evaluate
p3×p
Use the product rule an×am=an+m to simplify the expression
p3+1
Add the numbers
p4
27p3q4r4−27p4q4r3−27p3q3r5−(−27p4q3r4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
27p3q4r4−27p4q4r3−27p3q3r5+27p4q3r4
(27p3q4r4−27p4q4r3−27p3q3r5+27p4q3r4)(p−q)
Apply the distributive property
27p3q4r4p−27p3q4r4q−27p4q4r3p−(−27p4q4r3q)−27p3q3r5p−(−27p3q3r5q)+27p4q3r4p−27p4q3r4q
Multiply the terms
More Steps

Evaluate
p3×p
Use the product rule an×am=an+m to simplify the expression
p3+1
Add the numbers
p4
27p4q4r4−27p3q4r4q−27p4q4r3p−(−27p4q4r3q)−27p3q3r5p−(−27p3q3r5q)+27p4q3r4p−27p4q3r4q
Multiply the terms
More Steps

Evaluate
q4×q
Use the product rule an×am=an+m to simplify the expression
q4+1
Add the numbers
q5
27p4q4r4−27p3q5r4−27p4q4r3p−(−27p4q4r3q)−27p3q3r5p−(−27p3q3r5q)+27p4q3r4p−27p4q3r4q
Multiply the terms
More Steps

Evaluate
p4×p
Use the product rule an×am=an+m to simplify the expression
p4+1
Add the numbers
p5
27p4q4r4−27p3q5r4−27p5q4r3−(−27p4q4r3q)−27p3q3r5p−(−27p3q3r5q)+27p4q3r4p−27p4q3r4q
Multiply the terms
More Steps

Evaluate
q4×q
Use the product rule an×am=an+m to simplify the expression
q4+1
Add the numbers
q5
27p4q4r4−27p3q5r4−27p5q4r3−(−27p4q5r3)−27p3q3r5p−(−27p3q3r5q)+27p4q3r4p−27p4q3r4q
Multiply the terms
More Steps

Evaluate
p3×p
Use the product rule an×am=an+m to simplify the expression
p3+1
Add the numbers
p4
27p4q4r4−27p3q5r4−27p5q4r3−(−27p4q5r3)−27p4q3r5−(−27p3q3r5q)+27p4q3r4p−27p4q3r4q
Multiply the terms
More Steps

Evaluate
q3×q
Use the product rule an×am=an+m to simplify the expression
q3+1
Add the numbers
q4
27p4q4r4−27p3q5r4−27p5q4r3−(−27p4q5r3)−27p4q3r5−(−27p3q4r5)+27p4q3r4p−27p4q3r4q
Multiply the terms
More Steps

Evaluate
p4×p
Use the product rule an×am=an+m to simplify the expression
p4+1
Add the numbers
p5
27p4q4r4−27p3q5r4−27p5q4r3−(−27p4q5r3)−27p4q3r5−(−27p3q4r5)+27p5q3r4−27p4q3r4q
Multiply the terms
More Steps

Evaluate
q3×q
Use the product rule an×am=an+m to simplify the expression
q3+1
Add the numbers
q4
27p4q4r4−27p3q5r4−27p5q4r3−(−27p4q5r3)−27p4q3r5−(−27p3q4r5)+27p5q3r4−27p4q4r4
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
27p4q4r4−27p3q5r4−27p5q4r3+27p4q5r3−27p4q3r5+27p3q4r5+27p5q3r4−27p4q4r4
The sum of two opposites equals 0
More Steps

Evaluate
27p4q4r4−27p4q4r4
Collect like terms
(27−27)p4q4r4
Add the coefficients
0×p4q4r4
Calculate
0
0−27p3q5r4−27p5q4r3+27p4q5r3−27p4q3r5+27p3q4r5+27p5q3r4
Solution
−27p3q5r4−27p5q4r3+27p4q5r3−27p4q3r5+27p3q4r5+27p5q3r4
Show Solution
