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

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,
${\left(x - a\right)}^{2} = {x}^{2} - 2 a x + {a}^{2}$
and
${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$
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

$y = 6 x - 33$

#### Explanation:

We have;

$y = {\left(x - 4\right)}^{2} - {\left(x - 7\right)}^{2}$

Method 1 - Multiplying Out

We can multiply out both expressions to get:

$y = \left({x}^{2} - 8 x + 16\right) - \left({x}^{2} - 14 x + 49\right)$
$\setminus \setminus = {x}^{2} - 8 x + 16 - {x}^{2} + 14 x - 49$
$\setminus \setminus = 6 x - 33$

Method 2 - Difference of Two Squares#

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

${A}^{2} - {B}^{2} \equiv \left(A + B\right) \left(A - B\right)$

So we can write the expression as:

$y = \left\{\left(x - 4\right) + \left(x - 7\right)\right\} \cdot \left\{\left(x - 4\right) - \left(x - 7\right)\right\}$
$\setminus \setminus = \left\{x - 4 + x - 7\right\} \cdot \left\{x - 4 - x + 7\right\}$
$\setminus \setminus = \left(2 x - 11\right) \left(3\right)$
$\setminus \setminus = 6 x - 33$, as above