32ax + 12bx - 48ay - 18by

factor the polynomial

2(8a + 3b)(2x - 3y)

Step-by-step explanation:

32ax + 12bx - 48ay - 18by =

The first step in factoring is to factor out a common factor.

32, 12, -48, and -18 have the greatest common factor of 2.

= 2(16ax + 6bx - 24ay - 9by)

To factor a 4-term polynomial, factor it by parts. We factor out a common factor out of the first two terms, and we factor out a common factor out of the last two terms.

= 2[2x(8a + 3b) - 3y(8a + 3b)]

Now we have a common factor of 8a + 3b, so we factor that out.

= 2[(8a + 3b)(2x - 3y)]

Remove the unnecessary brackets.

= 2(8a + 3b)(2x - 3y)

Now we check every factor to confirm that no more factoring is possible.

There are no more common factors, and there are no methods of factoring binomials that are applicable, so the factoring is complete.

2(8a + 3b)(2x - 3y)

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step-by-step explanation: