Factor: 2xy + 6x - 4y - 12
a)(2x + 4) (y + 3)
b)(2x - 4) (y + 3)^2
c)(2x - 4) (y - 3)
d)(2x - 4) (y + 3)
2x(y+3)-4(y+3)
(2x-4)(y+3)
so the answer is d
(a) and (c) give a constant term of +12, so it cannot be right. (b) gives a constant term of -4*3²=-36...not good.
The only candidate (d) can be confirmed by expansion (multiplication).
To factor the expression 2xy + 6x - 4y - 12, follow these steps:
Step 1: Look for common factors among the terms. In this case, we can factor out a 2 from the first two terms and a -4 from the last two terms:
2xy + 6x - 4y - 12
= 2x(y + 3) - 4(y + 3)
Step 2: Notice that (y + 3) appears in both terms. Factor it out:
= (y + 3)(2x - 4)
Therefore, the correct factorization is d) (2x - 4) (y + 3).
To factor the expression 2xy + 6x - 4y - 12, we can use the method of grouping.
Step 1: Group the terms in pairs
Group the first two terms, 2xy and 6x, and the last two terms, -4y and -12.
(2xy + 6x) - (4y + 12)
Step 2: Factor out the common factors in each group.
In the first group, we can factor out 2x:
2x(y + 3) - (4y + 12)
In the second group, we can factor out 4:
2x(y + 3) - 4(y + 3)
Step 3: Identify the common binomial factor.
Both terms now share the common factor of (y + 3).
(y + 3)(2x - 4)
So, the correct factorization of the expression 2xy + 6x - 4y - 12 is (y + 3)(2x - 4).
Looking at the options provided:
a) (2x + 4)(y + 3) is not correct because it has the wrong signs in the binomial factors.
b) (2x - 4)(y + 3)^2 is not correct because it squares the (y + 3) factor, which is not present in the original expression.
c) (2x - 4)(y - 3) is not correct because the second binomial factor has the wrong sign.
d) (2x - 4)(y + 3) is the correct answer based on the factorization we obtained.
Therefore, the correct answer is option d) (2x - 4)(y + 3).