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

##### 2 Answers

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,

and

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.

# 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