Question
Simplify the expression
40a4−29a2+3
Evaluate
(5a2−3)(8a2−1)
Apply the distributive property
5a2×8a2−5a2×1−3×8a2−(−3×1)
Multiply the terms
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Evaluate
5a2×8a2
Multiply the numbers
40a2×a2
Multiply the terms
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Evaluate
a2×a2
Use the product rule an×am=an+m to simplify the expression
a2+2
Add the numbers
a4
40a4
40a4−5a2×1−3×8a2−(−3×1)
Any expression multiplied by 1 remains the same
40a4−5a2−3×8a2−(−3×1)
Multiply the numbers
40a4−5a2−24a2−(−3×1)
Any expression multiplied by 1 remains the same
40a4−5a2−24a2−(−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
40a4−5a2−24a2+3
Solution
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Evaluate
−5a2−24a2
Collect like terms by calculating the sum or difference of their coefficients
(−5−24)a2
Subtract the numbers
−29a2
40a4−29a2+3
Show Solution

Find the roots
a1=−515,a2=−42,a3=42,a4=515
Alternative Form
a1≈−0.774597,a2≈−0.353553,a3≈0.353553,a4≈0.774597
Evaluate
(5a2−3)(8a2−1)
To find the roots of the expression,set the expression equal to 0
(5a2−3)(8a2−1)=0
Separate the equation into 2 possible cases
5a2−3=08a2−1=0
Solve the equation
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Evaluate
5a2−3=0
Move the constant to the right-hand side and change its sign
5a2=0+3
Removing 0 doesn't change the value,so remove it from the expression
5a2=3
Divide both sides
55a2=53
Divide the numbers
a2=53
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±53
Simplify the expression
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Evaluate
53
To take a root of a fraction,take the root of the numerator and denominator separately
53
Multiply by the Conjugate
5×53×5
Multiply the numbers
5×515
When a square root of an expression is multiplied by itself,the result is that expression
515
a=±515
Separate the equation into 2 possible cases
a=515a=−515
a=515a=−5158a2−1=0
Solve the equation
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Evaluate
8a2−1=0
Move the constant to the right-hand side and change its sign
8a2=0+1
Removing 0 doesn't change the value,so remove it from the expression
8a2=1
Divide both sides
88a2=81
Divide the numbers
a2=81
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±81
Simplify the expression
More Steps

Evaluate
81
To take a root of a fraction,take the root of the numerator and denominator separately
81
Simplify the radical expression
81
Simplify the radical expression
221
Multiply by the Conjugate
22×22
Multiply the numbers
42
a=±42
Separate the equation into 2 possible cases
a=42a=−42
a=515a=−515a=42a=−42
Solution
a1=−515,a2=−42,a3=42,a4=515
Alternative Form
a1≈−0.774597,a2≈−0.353553,a3≈0.353553,a4≈0.774597
Show Solution
