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

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Full solution

Q. Find the product. Simplify your answer.\newline(4d−4)(4d+4)(4d - 4)(4d + 4)
  1. Identify Form: Identify the form of the expression.\newlineThe expression (4d−4)(4d+4)(4d - 4)(4d + 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 (4d−4)(4d+4)(4d - 4)(4d + 4) with (a−b)(a+b)(a - b)(a + b). a=4da = 4d b=4b = 4
  3. Apply Formula: Apply the difference of squares formula.\newlineUsing the formula (a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2, we get:\newline(4d−4)(4d+4)=(4d)2−(4)2(4d - 4)(4d + 4) = (4d)^2 - (4)^2
  4. Calculate Squares: Calculate the squares of aa and bb.(4d)2=16d2(4d)^2 = 16d^2(4)2=16(4)^2 = 16
  5. Subtract Squares: Subtract the square of bb from the square of aa.16d2−1616d^2 - 16
  6. Write Final Result: Write the final simplified result.\newlineThe product of (4d−4)(4d - 4) and (4d+4)(4d + 4) simplified is 16d2−1616d^2 - 16.

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