2y2-2y-4 = (2y-4)(y+1) when factored
8(2y^3 - z^2)(4y^6 + 2y^3z^2 + z^4)
x(y-10)+6(y-10) ^^^that's the first step, then: the x and 6 pair together, and one of the (y-10) leaves the expression so it becomes: (x+6)(y-10) this is referred to as Factoring by Grouping
Six factors: 1 2 4 13 26 52.
The factors of 2 are: 1, 2 The factors of 6 are: 1, 2, 3, 6 The common factors are: 1, 2
3x - 2y and 3x + 2y are in their simplest form. They don't factor.
2y2 - 2y - 24 has the factors (2y + 6) and (y - 4) There is a formula, but I always use trial and error. The factors of the non-x element need to be such that they can be added to give the middle element. So when you get 24, then you need to be looking at 2,12 - 3,8 - 4,6 When both the second and third element are minus values then there is a plus and a minus in the factors.
6+2y=8 -6 -6 2y=2 /2 /2 y=1
3x-2y=6 -2y=-3x+6 y=1.5x-3
4y+2 = 2y+6 4y-2y = 6-2 2y = 4 y = 2
x = 5 x-2y = 6 => x = 6+2y 6+2y = 5 2y = 5-6 2y = -1 y = -1/2 and x = 5 Point of intersection: (5, -1/2)
This reduces to the equation y=4x-3 (by the division of all factors by 2).
3x+2y=6 2y=-3x+6 y=-1.5x+3
5y-6 = 29-2y 5y+2y = 29+6 7y = 35 y = 5
solve for x -x-2y=6 -x=2y+6 x=-2y-6 plug in y=0 x=-6 when y is 0 therefore the x intercept is (-6,0)
If the two equations are (i) 4x + 2y = 12 and (ii) x + 2y = 6, proceed as follows: Rewrite (ii) as x = 6 - 2y; substitute this expression for x into (i) to result in 4(6 - 2y) + 2y = 12, or 24 - 8 y + 2y = 12, or - 6 y = 12 -24 = -12, or y = -12/-6 = 2. Then, back to (ii) again, x = 6 - 2(2) = 2.
3xy-2y=0 3xy=2y y=2y (3x) y/2y=3x 1/2=3x multiply across by 2 1=6x 1/6=x therefore substituting x=1/6 into 3xy-2y; 3(1/6)y-2y=0 1/2y=2y y=2y/0.5 0.5 aka 1/2 y=1