Which pair of forms is correct for (x^2-16) and (x^2-8x+16)?

Correct answer: ((x-4)(x+4)) and ((x-4)^2)

The direct answer is option A. For the first expression, use the difference-of-squares identity \(a^2-b^2=(a-b)(a+b)\): \(x^2-16=x^2-4^2=(x-4)(x+4)\). For the second, use \((x-4)^2=x^2-8x+16\), so \(x^2-8x+16=(x-4)^2\). Thus option A gives both forms correctly. Option B reverses the two forms: \((x-4)^2\) is not equal to \(x^2-16\), while \((x-4)(x+4)\) is not equal to the second expression. Option C uses \((x+4)^2=x^2+8x+16\) for the first, which has the wrong middle structure, even though its second form is correct. Option D is wrong because \((x-16)(x+1)=x^2-15x-16\), not \(x^2-16\), and \((x-8)^2=x^2-16x+64\), not the second expression. Memory cue: no middle term often signals difference of squares; a negative middle term and positive last term can signal \((x-4)^2\).