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Find the product. Simplify your answer.\newline(4t−2)(4t+2)(4t - 2)(4t + 2)

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the product. Simplify your answer.\newline(4t−2)(4t+2)(4t - 2)(4t + 2)
  1. Identify Special Case: Identify the special case that applies here.\newlineThe expression (4t−2)(4t+2)(4t - 2)(4t + 2) is in the form of (a−b)(a+b)(a - b)(a + b).\newlineSpecial case: (a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2
  2. Identify Values of aa and bb: Identify the values of aa and bb. Compare (4t−2)(4t+2)(4t - 2)(4t + 2) with (a−b)(a+b)(a - b)(a + b). a=4ta = 4t b=2b = 2
  3. Apply Difference of Squares Formula: Apply the difference of squares formula to expand (4t−2)(4t+2)(4t - 2)(4t + 2).\newline(a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2\newline(4t−2)(4t+2)=(4t)2−(2)2(4t - 2)(4t + 2) = (4t)^2 - (2)^2
  4. Simplify Expression: Simplify (4t)2−(2)2.(4t)^2 - (2)^2.(4t)2−(2)2=(4t×4t)−(2×2)(4t)^2 - (2)^2 = (4t \times 4t) - (2 \times 2)=16t2−4= 16t^2 - 4

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