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

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the product. Simplify your answer.\newline(2c+4)(2c−4)(2c + 4)(2c - 4)
  1. Identify Special Case: Identify the special case that applies to the given expression.\newlineThe expression (2c+4)(2c−4)(2c + 4)(2c - 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 of aa and bb: Identify the values of aa and bb. Compare (2c+4)(2c−4)(2c + 4)(2c - 4) with (a+b)(a−b)(a + b)(a - b). a=2ca = 2c b=4b = 4
  3. Apply Difference of Squares Formula: Apply the difference of squares formula to expand (2c+4)(2c−4)(2c + 4)(2c - 4).\newline(a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2\newline(2c+4)(2c−4)=(2c)2−42(2c + 4)(2c - 4) = (2c)^2 - 4^2
  4. Simplify Expression: Simplify (2c)2−42.(2c)^2 - 4^2.(2c)2−42=(2c⋅2c)−(4⋅4)(2c)^2 - 4^2 = (2c \cdot 2c) - (4 \cdot 4)=4c2−16= 4c^2 - 16

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