Question

How does one do the "Difference Of Perfect Squares?"

@TheSmartOne

Answer 1

Please dont just link me, explain it :P
@pooja195 @agent0smith @sammixboo @.Sam. @mathmate

Answer 2

Most of the time, we use difference of two squares to factor a polynomial expression, based on the identity:
a^2-b^2=(a+b)(a-b).

Examples:
\(x^2-49=x^2-7^2=(x+7)(x-7)\)
\(4x^2-25y^2=(2x)^2-(5y)^2=(2x+5y)(2x-5y)\)
If we recognize a perfect square, we could do more:
\(q^2+2q+1-p^2=(q+1)^2-p^2=(q+1+p)(q+1-p)\)
Be careful with common factors, as in
\(x^2z-4y^2z=z(x^2-(2y)^2)=(x+2y)(x-2y)z\)

Sometimes difference of two squares can be used to help calculation of products:
(x+4)(x-4)=x^2-16
48*52=(50-2)(50+2)=50^2-2^2=2500-4=2496
26*28=(27-1)(27+1)=27^2-1^2=729-1=728

Answer 3

Those are great examples @mathmate

Answer 4

@mathmate That makes more sense. But, Where do you get (x + 7) in the first problem? They are all negative? Or do they have to be opposite?

Answer 5

$$\Huge a^2-b^2=(a+b)(a-b)$$ let a = x and b = 7

Answer 6

Ah ok. Thank you :D

Answer 7

:D