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Dimas [21]
2 years ago
6

( x + 2 )^2 - ( y + 2 )^2

Mathematics
1 answer:
GarryVolchara [31]2 years ago
3 0

The difference of two squares factoring pattern states that a difference of two squares can be factored as follows:

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

So, whenever you recognize the two terms of a subtraction to be two squares, you can factor it as the sum of the roots multiplied by the difference of the roots.

In this case, the squares are obvious: (x+2)^2 is the square of x+2, and (y+2)^2 is the square of y+2

So, we can factor the expression as

(x+2)^2 - (y+2)^2 = [(x+2)+(y+2)] - [(x+2)+(y+2)]

(the round parenthesis aren't necessary, I used them only to make clear the two terms)

We can simplify the expression summing like terms:

(x+2)^2 - (y+2)^2 = [(x+2)+(y+2)][(x+2)-(y+2)] = (x+y+4)(x-y)

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