Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(y2−7)(y2+3)
Evaluate
y4−4y2−21
Rewrite the expression
y4+(3−7)y2−21
Calculate
y4+3y2−7y2−21
Rewrite the expression
y2×y2+y2×3−7y2−7×3
Factor out y2 from the expression
y2(y2+3)−7y2−7×3
Factor out −7 from the expression
y2(y2+3)−7(y2+3)
Solution
(y2−7)(y2+3)
Show Solution
Find the roots
y1=−3×i,y2=3×i,y3=−7,y4=7
Alternative Form
y1≈−1.732051i,y2≈1.732051i,y3≈−2.645751,y4≈2.645751
Evaluate
y4−4y2−21
To find the roots of the expression,set the expression equal to 0
y4−4y2−21=0
Factor the expression
(y2−7)(y2+3)=0
Separate the equation into 2 possible cases
y2−7=0y2+3=0
Solve the equation
More Steps
Evaluate
y2−7=0
Move the constant to the right-hand side and change its sign
y2=0+7
Removing 0 doesn't change the value,so remove it from the expression
y2=7
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±7
Separate the equation into 2 possible cases
y=7y=−7
y=7y=−7y2+3=0
Solve the equation
More Steps
Evaluate
y2+3=0
Move the constant to the right-hand side and change its sign
y2=0−3
Removing 0 doesn't change the value,so remove it from the expression
y2=−3
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±−3
Simplify the expression
More Steps
Evaluate
−3
Evaluate the power
3×−1
Evaluate the power
3×i
y=±(3×i)
Separate the equation into 2 possible cases
y=3×iy=−3×i
y=7y=−7y=3×iy=−3×i
Solution
y1=−3×i,y2=3×i,y3=−7,y4=7
Alternative Form
y1≈−1.732051i,y2≈1.732051i,y3≈−2.645751,y4≈2.645751
Show Solution