Factoring a difference of two squares?

OK

9a^2 - 64b^2
= (3a + 8b)(3a - 8b)
---------------

x^3y + 2x^2y^2 + xy^3 ; take out xy common factor

(xy) (x^2 + 2xy +y^2)
(xy)(x+y)(x+y)
or (xy)(x+y)^2

Hope that helps.

a million. x^2 - (y - z)^2 i think of the least complicated way of doing those style of questions is to handle them as a term. case in point: enable (y - z) = a So x^2 - (y - z)^2 = x^2 - a^2 = (x-a)(x+a) replace y - z back right into a. = [x-(y-z)][x+(y-z)] = (x - y +z)(x + y - z) Q2. that's corresponding to Q1. enable x = a + 2b (a + 2b)^2 - 9c^2 = x^2 - 9c^2 = (x - 3c)(x + 3c) = [(a+2b) - 3c][(a+2b) + 3c] = (a + 2b - 3c)(a + 2b + 3c)

a^2 - b^2 ≡ (a + b)(a - b)
a^2 + 2ab + b^2 ≡ (a + b)^2

1)
9a^2 - 64b^2
= (3a)^2 - (8b)^2
= (3a + 8b)(3a - 8b)

2)
x^3y + 2x^2y^2 + xy^3
= xy(x^2 + 2xy + y^2)
= xy(x + y)(x + y)
= xy(x + y)^2

Factors of the difference of squares x^2-y^2 are (x+y)(x-y). In your expression, x is 3a and y is 8b.

In the other polynomial, first extract xy to get (xy)(x^2 +2xy +y^2)

(xy)(x^2 +2xy +y^2) = (xy)(x + y)^2

x² - y² = (x + y)(x - y) ~ Therefore...
9a² - 64b² = (3a + 8b)(3a - 8b)

x³y + 2x²y² + xy³ --- Factorize each term...
(x)(x)(x)(y) + (2)(x)(x)(y)(y) + (x)(y)(y)(y) --- The GCF is xy...
xy(x² + 2xy + y²) --- Factor (x² + 2xy + y²)...
xy(x + y)(x + y) --- Simplify...
xy(x + y)²