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Hi,

Factor 16x^4 - 4y²

4(4x^4 - y²) =

4(2x - y)(2x + y) <==ANSWER

Factor 4x^4 - y²

(2x² - y)(2x² + y) <==ANSWER

Factor 4x² - 64y²

4(x² - 16y²) =

4(x - 4y)(x + 4y) <==ANSWER

Factor 9x² - 8y²

prime <==ANSWER

Factor x² - 16y²

(x - 4y)(x + 4y) <==ANSWER

I hope that helps!! :-)

An equation that is the difference of two squares

a^2 - b^2

factors as

( a + b ) ( a - b )

16x^4 - 4y^2 = ( 4x + 2y ) ( 4x - 2y )

4x^4 - y^2 = ( 2x^2 + y ) ( 2x^2 - y )

4x^2 - 64y^2 = ( 2x + 8y ) ( 2x - 8y )

9x^2 - 8y^2 = ( 3x + sqrt ( 8 )y ) ( 3x - sqrt ( 8 ) y )

x^2 - 16y^2 = ( x + 4y ) ( x - 4y )

Hi!

1. Factor 16x^4 - 4y^2

Find the common factor, which is 4. There are no common variables because they are both different.

Take 4 out and factor.

4(4x^4-y^2)

Now factor what is inside of the ( ).

4(2x^2-y)(2x^2+y)

2. Factor 4x^4 - y^2

The solution to this answer lies within number 1.

3. Factor 4x^2 - 64y^2

Find the common factor, which is 4.

Take 4 out and factor.

4(x^2-16y^2)

Now factor what is inside of the ( ).

4(x+4y)(x-4y)

4. 9x^2 - 8y^2 cannot be factored.

5. Factor x^2 - 16y^2

Use this formula: (a+b)(a-b) = a^2-b^2

I hoped I helped!

These problems are all "difference of squares." That is, every term is a square:

     16x⁴ = (4x²)²

     4y² = (2y)²

     4x⁴ = (2x²)²

     etc.

and each problem subtracts one square from another.

You need to recognize a "difference of squares" problem and know instantly how to solve it:

     a²x² - b²c² = (ax+bc)(ax-bc)

4(4x^4 - y^2) = 4(2x^2 + y)(2x^2 - y)

(2x^2 + y)(2x^2 - y)

4(x^2 - 16y^2) = 4(x + 4y)(x - 4y)

(3x + 2(2^-2)y)(3x - 2(2^-2)y)

(x + 4y)(x - 4y)

(4x^2-2y)(4x^2+2y)

(2x^2-y)(2x^2+y)

(2x-8y)(2x+8y)

(3x-sqrt(8)y)(3x+sqrt(8)y)

(x-4y)(x+4y)