# Which is a factor of 15xy - 45x - 6y + 18?

y - 2, 5x - 3, 5x - 2, y - 6

**Solution:**

The given equation is :

15xy - 45x - 6y + 18

= 15x(y - 3) - 6(y - 3)

= (y - 3)(15x - 6)

= (15x - 6)(y - 3)

= 3(5x - 2)(y - 3)

The three factors are 3, (5x - 2), and (y - 3) and one of them is (5x - 2) which is mentioned as one of the choices.

Another example of factorization is demonstrated below:

Factorize 12y^{2} - 27(y - 2x)^{2}

Expanding the given expression we have:

12y^{2} - 27(y - 2x)^{2}

= 12y^{2} - 27(y^{2} + 4x^{2 }- 4yx)

= 12y^{2} - 27y^{2} - 108x^{2} +108xy

= -15y^{2} - 108x^{2 }+ 108xy

= -3(5y^{2} - 36xy + 36x^{2})

Multiplying 5(coefficient of x^{2}) by 36(coefficient of y^{2}), we get 180. 30 & 6 are factors of 180 therefore we can factorize as follows

= -3(5y^{2} - 30xy - 6xy + 36x^{2})

= -3[5y(y - 6x) - 6x(y - 6x)]

= -3[(y - 6x)(5y - 6x)]

= -3(y - 6x)(5y - 6x)

Hence the factors are -3, (y - 6x) and (5y -6x)

## Which is a factor of 15xy - 45x - 6y + 18?

y - 2, 5x - 3, 5x - 2, y - 6

**Summary:**

(5x - 2) is a factor of 15xy - 45x - 6y + 18

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