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

Tucker Lewis

Tucker Lewis

Answered question

2022-01-31

What is the standard form of y=(x4)2(x+7)2?

Answer & Explanation

Iacopelli5co

Iacopelli5co

Beginner2022-02-01Added 15 answers

Explanation:
Rather than work out your homework for you, here is how to do it.
For any nonzero value of a,
(xa)2=x22ax+a2
and
(x+a)2=x2+2ax+a2
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.
budniji8d1

budniji8d1

Beginner2022-02-02Added 15 answers

Explanation:
We have;
y=(x4)2(x7)2
Method 1 - Multiplying Out
We can multiply out both expressions to get:
y=(x28x+16)(x214x+49)
=x28x+16x2+14x49
=6x-33
Method 2 - Difference of Two Squares#
As we have the difference of two squares we can use the identity:
A2B2(A+B)(AB)
So we can write the expression as:
y={(x4)+(x7)}{(x4)(x7)}
={x4+x7}{x4x+7}
=(2x-11)(3)
=6x-33, as above

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