Factoring Binomials: Difference of Two Squares

Factoring Binomials : Difference of Two Squares



Difference of Two Squares


X ^2 – Y^2=(X +Y ) ( X – Y)



The difference of two squares of two numbers is equal to the productof the sum and difference of the two numbers.



Example One :Factor64X^2-81^2

First let us inspect if the given problem is a difference of two squares. The numerical coefficients must be perfect squares. It means that their square root is an exact whole number. For literal coefficients, their exponents must be divisible by two. Only by meeting these conditions it can be factored as difference of two squares.


64 is a perfect square and its square root is 8. 81 is a perfect square and its square root is 9.

64^2 – 81^2 can be rewritten as ( 8X)^2-(9Y)^2therefore its factors are(8x + 9Y) (8X – 9Y).



Example Two :FactorX^8 – Y^8

X^8 – y^8=( x^4-)^2-(Y^4)^2

=( X^4 + Y^4) (X^4 – Y ^4)

=(X^4 + Y^4 ) (X^2 + Y^2) (X^2 – Y^2)

=(X^4 + Y^4 ) (X^2 + Y^2 ) (X +Y ) ( X – Y)



Example Three : Factor(a + 3b ) ^2 – 16c^4

(a + 3b)^2- 16 c^4=(a + 3b)^2 – (4c^2)^2

=(a + 3b+ 4c^2) (a + 3b – 4c^2)


Example Four : Factor49a^10b^8- 100c^6

49a^10b^8- 100c^6=( 7a^5b^4)^2-(10c^3)^2

=(7a^5b^4+- 10 c^3)(7a^5b^4- 10 c^3)



Example Five : Factor81X^12-256^Y^8

81X^12 – 256Y^8=(9X^6)^2-(16Y^4)

=(9X^6 + 16Y^4) (9X^6 – 16Y^4)

=(9X^6+ 16 Y^4) (3X^3 + 4Y^2) (3X^3 – 4Y^2)


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Comments 4 comments

Lord De Cross profile image

Lord De Cross 5 years ago

Excellent and well explained Cristina. Seen so many kids struggling with Algebra thru the years.Useful and voted up!

Lord


ronhi profile image

ronhi 5 years ago from Kenya

where were you when i was failing maths in school?


cristina327 profile image

cristina327 5 years ago from Manila Author

Thank you lord de cross for appreciating this hub. Blessings to you always and best regards.


cristina327 profile image

cristina327 5 years ago from Manila Author

HI ronhi thank you for dropping by. Regards.

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