Question
Factor the expression
3w(6−7w)(36+42w+49w2)
Evaluate
648w−1029w4
Factor out 3w from the expression
3w(216−343w3)
Solution
More Steps

Evaluate
216−343w3
Rewrite the expression in exponential form
63−(7w)3
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(6−7w)(62+6×7w+(7w)2)
Evaluate
(6−7w)(36+6×7w+(7w)2)
Evaluate
(6−7w)(36+42w+(7w)2)
Evaluate
More Steps

Evaluate
(7w)2
To raise a product to a power,raise each factor to that power
72w2
Evaluate the power
49w2
(6−7w)(36+42w+49w2)
3w(6−7w)(36+42w+49w2)
Show Solution

Find the roots
w1=0,w2=76
Alternative Form
w1=0,w2=0.8˙57142˙
Evaluate
648w−1029w4
To find the roots of the expression,set the expression equal to 0
648w−1029w4=0
Factor the expression
3w(216−343w3)=0
Divide both sides
w(216−343w3)=0
Separate the equation into 2 possible cases
w=0216−343w3=0
Solve the equation
More Steps

Evaluate
216−343w3=0
Move the constant to the right-hand side and change its sign
−343w3=0−216
Removing 0 doesn't change the value,so remove it from the expression
−343w3=−216
Change the signs on both sides of the equation
343w3=216
Divide both sides
343343w3=343216
Divide the numbers
w3=343216
Take the 3-th root on both sides of the equation
3w3=3343216
Calculate
w=3343216
Simplify the root
More Steps

Evaluate
3343216
To take a root of a fraction,take the root of the numerator and denominator separately
33433216
Simplify the radical expression
33436
Simplify the radical expression
76
w=76
w=0w=76
Solution
w1=0,w2=76
Alternative Form
w1=0,w2=0.8˙57142˙
Show Solution
