Question

Given that b≠0 , for what value of x are the expressions (x−b)(x+b) and x^2 −x equivalent?

Answer 1

To find the value of x for which the expressions (x−b)(x+b) and x^2 −x are equivalent, we need to set the two expressions equal to each other and solve for x.

Step-by-step explanation:

To find the value of x for which the expressions (x−b)(x+b) and x^2 −x are equivalent, we need to set the two expressions equal to each other and solve for x.

Setting (x−b)(x+b) = x^2 −x, we can expand the left side of the equation: x^2-b^2 = x^2 −x.

Now, we can subtract x^2 from both sides to get: -b^2 = -x.

Finally, we can multiply both sides by -1 to isolate x and we get x = b^2.

Answer 2

`\stackrel{ \textit{difference of squares} }{(x-b)(x+b)}~~ = ~~x^2-x\implies x^2-b^2=x^2-x \\\\\\ -b^2=-x\implies b^2=x\implies b=\pm√(x)`