Multiply the binomials.
$(x^2-1)(x^2+1)$

• A. $x^2-1$
• B. $x^4+2x^2-1$
• C. $x^4-2x^2+1$
• D. $x^4-1$

Answer: (D)

Verified step by step guidance

1. Recognize that you are asked to multiply two binomials: \(\left(x^{2} - 1\right) \times \left(x^{2} + 1\right)\).
2. Apply the distributive property (also known as FOIL for binomials) by multiplying each term in the first binomial by each term in the second binomial: \(x^{2} \times x^{2}\), \(x^{2} \times 1\), \(-1 \times x^{2}\), and \(-1 \times 1\).
3. Write out the products explicitly: \(x^{2} \times x^{2} = x^{4}\), \(x^{2} \times 1 = x^{2}\), \(-1 \times x^{2} = -x^{2}\), and \(-1 \times 1 = -1\).
4. Combine all these terms into a single expression: \(x^{4} + x^{2} - x^{2} - 1\).
5. Simplify the expression by combining like terms \(x^{2}\) and \(-x^{2}\), which cancel each other out, leaving you with \(x^{4} - 1\).