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Find the product. Simplify your answer.\newline(2r+3)(2r−4)(2r + 3)(2r - 4)

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Full solution

Q. Find the product. Simplify your answer.\newline(2r+3)(2r−4)(2r + 3)(2r - 4)
  1. Apply Distributive Property: First, we need to apply the distributive property to multiply each term in the first binomial by each term in the second binomial.\newline(2r+3)(2r−4)=2r(2r)+2r(−4)+3(2r)+3(−4)(2r + 3)(2r - 4) = 2r(2r) + 2r(-4) + 3(2r) + 3(-4)
  2. Perform Multiplication: Now, we perform the multiplication for each term.\newline2r(2r)=4r22r(2r) = 4r^2\newline2r(−4)=−8r2r(-4) = -8r\newline3(2r)=6r3(2r) = 6r\newline3(−4)=−123(-4) = -12
  3. Combine Like Terms: Next, we combine the like terms from the multiplication. 4r2−8r+6r−124r^2 - 8r + 6r - 12
  4. Final Simplified Expression: Combining the like terms −8r-8r and 6r6r gives us: 4r2−2r−124r^2 - 2r - 12

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