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Find the product. Simplify your answer.\newline(z+2)(z−2)(z + 2)(z - 2)

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Full solution

Q. Find the product. Simplify your answer.\newline(z+2)(z−2)(z + 2)(z - 2)
  1. Apply formula: Apply the difference of squares formula.\newlineThe expression (z+2)(z−2)(z + 2)(z - 2) is a difference of squares, which can be simplified using the formula a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b), where a=za = z and b=2b = 2.\newlineSo, (z+2)(z−2)=z2−22(z + 2)(z - 2) = z^2 - 2^2.
  2. Calculate squares: Calculate the squares and simplify the expression.\newlineNow we calculate z2z^2 and 222^2.\newlinez2z^2 is the square of zz, and 222^2 is the square of 22, which is 44.\newlineSo, (z+2)(z−2)=z2−4(z + 2)(z - 2) = z^2 - 4.
  3. Write final form: Write the final simplified form.\newlineThe final simplified form of the product is z2−4z^2 - 4.

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