Question
Simplify the expression
162w5−8w−16
Evaluate
9w3×18w2−8w−16
Solution
More Steps

Evaluate
9w3×18w2
Multiply the terms
162w3×w2
Multiply the terms with the same base by adding their exponents
162w3+2
Add the numbers
162w5
162w5−8w−16
Show Solution

Factor the expression
2(3w−2)(27w4+18w3+12w2+8w+4)
Evaluate
9w3×18w2−8w−16
Multiply
More Steps

Evaluate
9w3×18w2
Multiply the terms
162w3×w2
Multiply the terms with the same base by adding their exponents
162w3+2
Add the numbers
162w5
162w5−8w−16
Rewrite the expression
2×81w5−2×4w−2×8
Factor out 2 from the expression
2(81w5−4w−8)
Solution
More Steps

Evaluate
81w5−4w−8
Calculate
81w5+54w4+36w3+24w2+12w−54w4−36w3−24w2−16w−8
Rewrite the expression
3w×27w4+3w×18w3+3w×12w2+3w×8w+3w×4−2×27w4−2×18w3−2×12w2−2×8w−2×4
Factor out 3w from the expression
3w(27w4+18w3+12w2+8w+4)−2×27w4−2×18w3−2×12w2−2×8w−2×4
Factor out −2 from the expression
3w(27w4+18w3+12w2+8w+4)−2(27w4+18w3+12w2+8w+4)
Factor out 27w4+18w3+12w2+8w+4 from the expression
(3w−2)(27w4+18w3+12w2+8w+4)
2(3w−2)(27w4+18w3+12w2+8w+4)
Show Solution

Find the roots
w=32
Alternative Form
w=0.6˙
Evaluate
9w3×18w2−8w−16
To find the roots of the expression,set the expression equal to 0
9w3×18w2−8w−16=0
Multiply
More Steps

Multiply the terms
9w3×18w2
Multiply the terms
162w3×w2
Multiply the terms with the same base by adding their exponents
162w3+2
Add the numbers
162w5
162w5−8w−16=0
Factor the expression
2(3w−2)(27w4+18w3+12w2+8w+4)=0
Divide both sides
(3w−2)(27w4+18w3+12w2+8w+4)=0
Separate the equation into 2 possible cases
3w−2=027w4+18w3+12w2+8w+4=0
Solve the equation
More Steps

Evaluate
3w−2=0
Move the constant to the right-hand side and change its sign
3w=0+2
Removing 0 doesn't change the value,so remove it from the expression
3w=2
Divide both sides
33w=32
Divide the numbers
w=32
w=3227w4+18w3+12w2+8w+4=0
Solve the equation
w=32w∈/R
Solution
w=32
Alternative Form
w=0.6˙
Show Solution
