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Question
x^{2}\times 3x-3
Simplify the expression
3x^{3}-3
Evaluate
x^{2}\times 3x-3
Solution
More Steps
Evaluate
x^{2}\times 3x
Multiply the terms with the same base by adding their exponents
x^{2+1}\times 3
Add the numbers
x^{3}\times 3
Use the commutative property to reorder the terms
3x^{3}
3x^{3}-3
Show Solutions
Factor the expression
3\left(x-1\right)\left(x^{2}+x+1\right)
Evaluate
x^{2}\times 3x-3
Evaluate
More Steps
Evaluate
x^{2}\times 3x
Multiply the terms with the same base by adding their exponents
x^{2+1}\times 3
Add the numbers
x^{3}\times 3
Use the commutative property to reorder the terms
3x^{3}
3x^{3}-3
\text{Factor out }3\text{ from the expression}
3\left(x^{3}-1\right)
Solution
More Steps
Evaluate
x^{3}-1
Rewrite the expression in exponential form
x^{3}-1^{3}
\text{Use }a^3-b^3=(a-b)(a^2+ab+b^2)\text{ to factor the expression}
\left(x-1\right)\left(x^{2}+x\times 1+1^{2}\right)
Any expression multiplied by 1 remains the same
\left(x-1\right)\left(x^{2}+x+1^{2}\right)
1 raised to any power equals to 1
\left(x-1\right)\left(x^{2}+x+1\right)
3\left(x-1\right)\left(x^{2}+x+1\right)
Show Solutions
Find the roots
x=1
Evaluate
x^{2}\times 3x-3
To find the roots of the expression,set the expression equal to 0
x^{2}\times 3x-3=0
Multiply
More Steps
Multiply the terms
x^{2}\times 3x
Multiply the terms with the same base by adding their exponents
x^{2+1}\times 3
Add the numbers
x^{3}\times 3
Use the commutative property to reorder the terms
3x^{3}
3x^{3}-3=0
Move the constant to the right-hand side and change its sign
3x^{3}=0+3
Removing 0 doesn't change the value,so remove it from the expression
3x^{3}=3
Divide both sides
\frac{3x^{3}}{3}=\frac{3}{3}
Divide the numbers
x^{3}=\frac{3}{3}
Divide the numbers
More Steps
Evaluate
\frac{3}{3}
Reduce the numbers
\frac{1}{1}
Calculate
1
x^{3}=1
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{x^{3}}=\sqrt[3]{1}
Calculate
x=\sqrt[3]{1}
Solution
x=1
Show Solutions
