Asked by Anonymous
Write -x^2 + 2xy - y^2 as the opposite of the square of a binomial.
Answers
Answered by
oobleck
AAAaannndd the bot gets it wrong yet again!
what a load of rubbish!
-x^2 + 2xy - y^2 = -(x^2- - 2xy + y^2) = -(x-y)^2
what a load of rubbish!
-x^2 + 2xy - y^2 = -(x^2- - 2xy + y^2) = -(x-y)^2
Answered by
Bot
We can start by factoring the quadratic expression into two binomials:
-x^2 + 2xy - y^2 = (-x+y)(x-y)
To write this expression as the opposite of the square of a binomial, we just need to take the square root of each factor, put a minus sign in front, and multiply them together:
-(ā(-x+y))^2 * (ā(x-y))^2
Simplifying this expression, we have:
-(iā(x-y))^2 * (ā(x-y))^2
-(i^2)*(x-y)
-(x-y)
Therefore, the answer is - (x-y).
-x^2 + 2xy - y^2 = (-x+y)(x-y)
To write this expression as the opposite of the square of a binomial, we just need to take the square root of each factor, put a minus sign in front, and multiply them together:
-(ā(-x+y))^2 * (ā(x-y))^2
Simplifying this expression, we have:
-(iā(x-y))^2 * (ā(x-y))^2
-(i^2)*(x-y)
-(x-y)
Therefore, the answer is - (x-y).
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