# The product of the sum and difference of the same two terms is equal to what?

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i need help with summer school.

### Other Answers (3)

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(x + y)(x - y)

x^2 - xy + xy - y^2

The middle terms cancel

x^2 - y^2

The product of the sum and the difference fo the same two terms is equal to the difference of the terms squared. Notice that the order of the terms is relevant. If y were the first term, then the outcome would be y^2 - x^2 . It's called a "perfect square", or:

The Difference of Squares

[check: (2+3)(2-3) = (5)(-1) = -5 and (2)^2-(3)^2 = 4 - 9 = -5 ]

[note: x^2 - y^2 is not the same as (x - y)^2 ] -
Suppose we call the two terms a and b. Then the product of the sum and difference is:

(a + b)(a - b)

Expand (FOIL):

= a² - ab + ab - b²

The ab's cancel out, so you're left with:

= a² - b², which is the difference of the squares. -
The difference of squares.

(a+b)(a-b) = a^2 - b^2

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