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

2 Answers
Mar 25, 2017

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.

Mar 27, 2017

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