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Find the product. Simplify your answer.\newline(4z+4)(4z−4)(4z + 4)(4z - 4)

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Full solution

Q. Find the product. Simplify your answer.\newline(4z+4)(4z−4)(4z + 4)(4z - 4)
  1. Identify Form: Identify the form of the expression.\newlineThe expression (4z+4)(4z−4)(4z + 4)(4z - 4) is in the form of (a+b)(a−b)(a + b)(a - b), which is a difference of squares.\newlineSpecial case: (a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2
  2. Identify Values: Identify the values of aa and bb. Compare (4z+4)(4z−4)(4z + 4)(4z - 4) with (a+b)(a−b)(a + b)(a - b). a=4za = 4z b=4b = 4
  3. Apply Formula: Apply the difference of squares formula.\newlineUsing the values of aa and bb, we can expand (4z+4)(4z−4)(4z + 4)(4z - 4) using the formula.\newline(4z+4)(4z−4)=(4z)2−(4)2(4z + 4)(4z - 4) = (4z)^2 - (4)^2
  4. Simplify Expression: Simplify the expression.\newline(4z)2−(4)2(4z)^2 - (4)^2\newline= (4z×4z)−(4×4)(4z \times 4z) - (4 \times 4)\newline= 16z2−1616z^2 - 16

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