Questions: Sabendo que x · y=15, quanto vale (x-y)^2-(x+y)^2 ? Escolha uma opção: a. 48 b. 16 c. -16 d. -48 e. -60

Solution Steps

To solve the expression \((x-y)^{2}-(x+y)^{2}\), we can use the identity for the difference of squares: \(a^2 - b^2 = (a-b)(a+b)\). Here, \(a = x-y\) and \(b = x+y\). Therefore, the expression becomes \((x-y-x-y)(x-y+x+y)\), which simplifies to \(-4xy\). Given that \(x \cdot y = 15\), substitute this value into the expression to find the result.

We need to evaluate the expression \((x-y)^{2}-(x+y)^{2}\).

The expression \((x-y)^{2}-(x+y)^{2}\) can be rewritten using the difference of squares identity: \[ a^2 - b^2 = (a-b)(a+b) \] where \(a = x-y\) and \(b = x+y\). Thus, the expression becomes: \[ (x-y-x-y)(x-y+x+y) = (-2y)(2x) = -4xy \]

We are given that \(x \cdot y = 15\). Substitute this into the expression: \[ -4xy = -4 \times 15 = -60 \]

Final Answer