Question

Please explain this?

If
12y^2 -7y-12=0 (1)

Then
12y^2 -16y+9y-12=0 (2)

Please explain (2)

Answer 1

The equations are the same

Explanation:

In equation 2, they didn't do the subtraction:

`-16y+9y = -7y`

`12y^2 -16y+9y -12 -= 12y^2 -7y-12=0`

Answer 2

for factorisation by grouping

Explanation:

they are the same equation, but the second makes it easier to factorise the expression, by grouping.

`12y^2-7y -12 = 0`

the first step when factorising a quadratic expression by grouping is to multiply the first and last term together.

`12 * -12 = -144`

the next step is to find two numbers that add to make the second term, and multiply to make the product of the first and last term.

`-16 + 9 = -7`

`-16 * 9 = -144`

this is why `12y^2-7y -12 = 0` can later be written as `12y^2 + 16y - 9y - 12 = 0`.

see below for solution of `y:`

`12y^2 + 16y - 9y - 12 = 0`

`12y^2+16y = 4y(3y+4)`

`-9y - 12 = -3(3y+4)`

`12y^2 + 16y - 9y - 12 = 4y(3y+4) -3(3y+4)`

`3y+4` is a common factor, so it can be bracketed off.

`4y(3y+4) -3(3y+4) = (4y-3)(3y+4)`

in the equation to solve for `x`, `(4y-3)(3y+4) = 0`

`n * 0 = 0`

if either `4y-3` or `3y+4` is `0`, the product of both will be `0`.

`4y-3 = 0`

`4y = 0+3 = 3`

`y = 3/4`

`3y+4 =0`

`3y = -4`

`y = -4/3`

this gives the two values of `y:` `3/4` and `-4/3`.