Question

What is the standard form of `y= (6x-4)(x+3)-(2x-1)(3x-2)`?

Answer 1

`21x-y=14`

Explanation:

To find the standard form, you have to multiply the content of the parenthesis. First, the first pair:
The first number of the first parenthesis multiplies the numbers in the second one: `6x * x + 6x * 3 = 6x^2 + 18x`. Then we add the multiplication of the second number in the first parenthesis by the numbers in the second one: `-4 * x + (-4) * 3 = -4x -12` and join them
:
`6x^2 +18x -4x -12 = 6x^2 +14x -12`.

Now, just do the same with the second pair:

`2x * 3x + 2x * (-2) = 6x^2 -4x` and `(-1) * (3x) + (-1) * (-2) = -3x + 2`

And now put them together: `6x^2 -4x -3x +2 = 6x^2 -7x +2`

And, finally, join the content from the two parenthesis:
`y=6x^2 +14x -12 -(6x^2 -7x +2)=`
`y=6x^2 - 6x^2+14x+7x-12-2 =`
`y=21x -14`

The standard form of a linear equation is `Ax+By=C`

Therefore, we can re-arrange the terms to bring the equation in its standard form as:

`21x-y=14`