Question

What is the standard form of `y= (x-4)^2-(x+7)^2`?

Answer 1

Use FOIL and simplify. It is a line.

Explanation:

Rather than work out your homework for you, here is how to do it.
For any nonzero value of a,
`(x-a)^2 = x^2 - 2ax + a^2`
and
`(x+a)^2 = x^2 + 2ax + a^2`
When you subtract the two expressions, do not forget to distribute the - sign to all three terms.
Combine like terms, and you will have a line in slope-intercept form.
If you would like to put the line into standard form, then when you have done all of the above, subtract the term containing x from the right side, so that it "moves over" to the left side. The Standard Form of a linear equation is
Ax + By = C.

Answer 2

`y = 6x-33`

Explanation:

We have;

`y=(x-4)^2-(x-7)^2`

Method 1 - Multiplying Out

We can multiply out both expressions to get:

`y = (x^2-8x+16) - (x^2-14x+49)`
`\ \ = x^2-8x+16 - x^2+14x-49`
`\ \ = 6x-33`

Method 2 - Difference of Two Squares#

As we have the difference of two squares we can use the identity:

`A^2-B^2-=(A+B)(A-B)`

So we can write the expression as:

`y = {(x-4)+(x-7)} * {(x-4)-(x-7)}`
`\ \ = {x-4+x-7} * {x-4-x+7}`
`\ \ = (2x-11)(3)`
`\ \ = 6x-33`, as above