Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
a3−2a2+4a−3
Evaluate
(a−1)a2−(a−3)(a−1)
Multiply the terms
a2(a−1)−(a−3)(a−1)
Rewrite the expression
a2(a−1)+(−a+3)(a−1)
Expand the expression
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Calculate
a2(a−1)
Apply the distributive property
a2×a−a2×1
Multiply the terms
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Evaluate
a2×a
Use the product rule an×am=an+m to simplify the expression
a2+1
Add the numbers
a3
a3−a2×1
Any expression multiplied by 1 remains the same
a3−a2
a3−a2+(−a+3)(a−1)
Expand the expression
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Calculate
(−a+3)(a−1)
Apply the distributive property
−a×a−(−a×1)+3a−3×1
Multiply the terms
−a2−(−a×1)+3a−3×1
Any expression multiplied by 1 remains the same
−a2−(−a)+3a−3×1
Any expression multiplied by 1 remains the same
−a2−(−a)+3a−3
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−a2+a+3a−3
Add the terms
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Evaluate
a+3a
Collect like terms by calculating the sum or difference of their coefficients
(1+3)a
Add the numbers
4a
−a2+4a−3
a3−a2−a2+4a−3
Solution
More Steps
Evaluate
−a2−a2
Collect like terms by calculating the sum or difference of their coefficients
(−1−1)a2
Subtract the numbers
−2a2
a3−2a2+4a−3
Show Solution
Factor the expression
(a2−a+3)(a−1)
Evaluate
(a−1)a2−(a−3)(a−1)
Multiply the terms
a2(a−1)−(a−3)(a−1)
Rewrite the expression
a2(a−1)+(−a+3)(a−1)
Solution
(a2−a+3)(a−1)
Show Solution
Find the roots
a1=21−211i,a2=21+211i,a3=1
Alternative Form
a1≈0.5−1.658312i,a2≈0.5+1.658312i,a3=1
Evaluate
(a−1)(a2)−(a−3)(a−1)
To find the roots of the expression,set the expression equal to 0
(a−1)(a2)−(a−3)(a−1)=0
Calculate
(a−1)a2−(a−3)(a−1)=0
Multiply the terms
a2(a−1)−(a−3)(a−1)=0
Rewrite the expression
a2(a−1)+(−a+3)(a−1)=0
Calculate
More Steps
Evaluate
a2(a−1)+(−a+3)(a−1)
Expand the expression
More Steps
Calculate
a2(a−1)
Apply the distributive property
a2×a−a2×1
Multiply the terms
a3−a2×1
Any expression multiplied by 1 remains the same
a3−a2
a3−a2+(−a+3)(a−1)
Expand the expression
More Steps
Calculate
(−a+3)(a−1)
Apply the distributive property
−a×a−(−a×1)+3a−3×1
Multiply the terms
−a2−(−a×1)+3a−3×1
Any expression multiplied by 1 remains the same
−a2−(−a)+3a−3×1
Any expression multiplied by 1 remains the same
−a2−(−a)+3a−3
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−a2+a+3a−3
Add the terms
−a2+4a−3
a3−a2−a2+4a−3
Subtract the terms
More Steps
Evaluate
−a2−a2
Collect like terms by calculating the sum or difference of their coefficients
(−1−1)a2
Subtract the numbers
−2a2
a3−2a2+4a−3
a3−2a2+4a−3=0
Factor the expression
(a−1)(a2−a+3)=0
Separate the equation into 2 possible cases
a−1=0a2−a+3=0
Solve the equation
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Evaluate
a−1=0
Move the constant to the right-hand side and change its sign
a=0+1
Removing 0 doesn't change the value,so remove it from the expression
a=1
a=1a2−a+3=0
Solve the equation
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Evaluate
a2−a+3=0
Substitute a=1,b=−1 and c=3 into the quadratic formula a=2a−b±b2−4ac
a=21±(−1)2−4×3
Simplify the expression
More Steps
Evaluate
(−1)2−4×3
Evaluate the power
1−4×3
Multiply the numbers
1−12
Subtract the numbers
−11
a=21±−11
Simplify the radical expression
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Evaluate
−11
Evaluate the power
11×−1
Evaluate the power
11×i
a=21±11×i
Separate the equation into 2 possible cases
a=21+11×ia=21−11×i
Simplify the expression
a=21+211ia=21−11×i
Simplify the expression
a=21+211ia=21−211i
a=1a=21+211ia=21−211i
Solution
a1=21−211i,a2=21+211i,a3=1
Alternative Form
a1≈0.5−1.658312i,a2≈0.5+1.658312i,a3=1
Show Solution