2x2 + 6xy = 2x (x + 3y)
Since 3y^2 is a factor of 18y^2, it is automatically the GCF.
The GCF of 12y^3 and 15y^2 is 3y^2
Well, honey, to factor 4x + 12y, you can start by taking out the greatest common factor, which in this case is 4. So you're left with 4(x + 3y). And that's all she wrote!
Since 3y2 can evenly divide 24y3, 3y2 must be the greatest common factor, since the greatest common factor cannot be larger than the smaller of the two numbers. But, we can also look at a factorization of both numbers. We can tell that 3y2 = 3 x y2. We can tell that 24y3 = 3 x 8 x y3 = 3 x 23 x y2 x y. These numbers have in common 3 and y2, so 3y2 is the greatest common factor.
If that's +6xy, the answer is 2x(x + 3y) If that's -6xy, the answer is 2x(x - 3y)
2x2 + 6xy = 2x (x + 3y)
(a + x - 3y)(a - x + 3y)
The GCF is 3.
(3x + 3y)(x + y) = 3(x + y)2
3y(3x - 2y)(9x^2 + 6xy + 4y^2)
x^2(2x - 3y)(4x^2 + 6xy + 9y^2)
3y2 - 2y + 6xy - 4x = y(3y - 2) + 2x(3y - 2) = (y + 2x)*(3y - 2)
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Since 3y^2 is a factor of 18y^2, it is automatically the GCF.
(3x + 3y)(x + y) or 3(x + y)2
The quotient of 2x and 3y is = 6xy