Factor completely: 9x³y² - 36x Factor by grouping: 6x - 6y - 5ax + 5ay?

(6-5a)(x-y)


.

Factor 9x out of both terms

9x(x^2y^2 - 4)

The second is the difference to two squares

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

9x(xy+2)(xy-2)

Factor 6 out of the first two terms

6(x-y)

Factor -5a out of the third and fourth

-5a(x - y)

Since there is the common factor of (x-y)

(6 - 5a)(x-y)

1)
9x^3y^2 - 36x
= 9(x^3y^2 - 4x)
= 9x(x^2y^2 - 4)
= 9x(x^2y^2 + 2xy - 2xy - 4)
= 9x[(x^2y^2 + 2xy) - (2xy + 4)]
= 9x[xy(xy + 2) - 2(xy + 2)]
= 9x(xy + 2)(xy - 2)

2)
6x - 6y - 5ax + 5ay
= (6x - 6y) - (5ax - 5ay)
= 6(x - y) - 5a(x - y)
= (x - y)(6 - 5a)

9x(x^2 y^2 - 4)
9x(xy - 2) (xy + 2)


6x - 6y - 5ax + 5ay

= 6(x - y) - 5a (x - y)

= (6 - 5a) (x - y)

9x (x^2y^2 - 4)
=9x(xy-2)(xy+2)

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6(x-y) - 5a(x-y)

(6 -- 5a) ( x-y)

1. 9x(xy-2)(xy+2)

2. 6(x-y) - 5a(x-y) = (6-5a)(x-y)

9x(x^2y^2 - 4)
9x(xy+2)(xy-2)

6(x-y) - 5a(x-y)
(6-5a)(x-y)

9x (x²y - 4)

6(x-y) - 5a (x-y)