Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
8520x4−102240x3+306720x2
Evaluate
(x2−6x)×213(x2−6x)×40
Multiply the terms
(x2−6x)×8520(x2−6x)
Multiply the first two terms
8520(x2−6x)(x2−6x)
Multiply the terms
8520(x2−6x)2
Expand the expression
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Evaluate
(x2−6x)2
Use (a−b)2=a2−2ab+b2 to expand the expression
(x2)2−2x2×6x+(6x)2
Calculate
x4−12x3+36x2
8520(x4−12x3+36x2)
Apply the distributive property
8520x4−8520×12x3+8520×36x2
Multiply the numbers
8520x4−102240x3+8520×36x2
Solution
8520x4−102240x3+306720x2
Show Solution
Factor the expression
8520x2(x−6)2
Evaluate
(x2−6x)×213(x2−6x)×40
Multiply the terms
(x2−6x)×8520(x2−6x)
Multiply the first two terms
8520(x2−6x)(x2−6x)
Multiply the terms
8520(x2−6x)2
Solution
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Evaluate
(x2−6x)2
Factor the expression
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Evaluate
x2−6x
Rewrite the expression
x×x−x×6
Factor out x from the expression
x(x−6)
(x(x−6))2
Evaluate the power
x2(x−6)2
8520x2(x−6)2
Show Solution
Find the roots
x1=0,x2=6
Evaluate
(x2−6x)×213(x2−6x)×40
To find the roots of the expression,set the expression equal to 0
(x2−6x)×213(x2−6x)×40=0
Multiply the terms
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Multiply the terms
(x2−6x)×213(x2−6x)×40
Multiply the terms
(x2−6x)×8520(x2−6x)
Multiply the first two terms
8520(x2−6x)(x2−6x)
Multiply the terms
8520(x2−6x)2
8520(x2−6x)2=0
Rewrite the expression
(x2−6x)2=0
The only way a power can be 0 is when the base equals 0
x2−6x=0
Factor the expression
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Evaluate
x2−6x
Rewrite the expression
x×x−x×6
Factor out x from the expression
x(x−6)
x(x−6)=0
When the product of factors equals 0,at least one factor is 0
x=0x−6=0
Solve the equation for x
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Evaluate
x−6=0
Move the constant to the right-hand side and change its sign
x=0+6
Removing 0 doesn't change the value,so remove it from the expression
x=6
x=0x=6
Solution
x1=0,x2=6
Show Solution