# How do you solve #8y^4 - 4y^2 = 0#?

##### 3 Answers

#### Explanation:

Factor out

So

Or

#### Explanation:

Find the factors first., look for a common factor before doing anything else.

Either of the factors could be equal to 0.

Make two equations and solve each.

if

#### Explanation:

First, notice that both terms have a common factor of

#8y^4-4y^2=0#

#4y^2((8y^4)/(4y^2)-(4y^2)/(4y^2))=0#

#4y^2(2y^2-1)=0#

We now have two different terms being multiplied to equal

We can use the "Zero Factor Property" here, which basically states that if factors are being multiplied to equal

So here, we know that:

#{(4y^2=0),(2y^2-1=0):}#

Solving the first:

#4y^2=0#

This boils down to our first solution:

#barul|color(white)(a/a)y=0color(white)(a/a)|#

Solving the second:

#2y^2-1=0#

#2y^2=1#

#y^2=1/2#

Taking the square root of both sides (remember to allow positive and negative solutions):

#y=+-sqrt(1/2)=+-1/sqrt2=+-sqrt2/2#

Giving

#barul|color(white)(a/a)y=sqrt2/2color(white)(a/a)|#

#barul|color(white)(a/a)y=-sqrt2/2color(white)(a/a)|#