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Find the product. Simplify your answer. (3q+1)(3q-1)

Find the product. Simplify your answer.\newline(3q+1)(3q−1) (3 q+1)(3 q-1)

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Multiply two binomials: special casesright chevron icon

Full solution

Q. Find the product. Simplify your answer.\newline(3q+1)(3q−1) (3 q+1)(3 q-1)
  1. Identify special case: Identify the special case for the product (3q+1)(3q−1)(3q+1)(3q-1). This product is in the form of (a+b)(a−b)(a+b)(a-b), which is a difference of squares. Special 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 (3q+1)(3q−1)(3q+1)(3q-1) with (a+b)(a−b)(a+b)(a-b). a=3qa = 3q b=1b = 1
  3. Apply difference of squares formula: Apply the difference of squares formula to expand (3q+1)(3q−1)(3q+1)(3q-1).\newline(a+b)(a−b)=a2−b2(a+b)(a-b) = a^2 - b^2\newline(3q+1)(3q−1)=(3q)2−(1)2(3q+1)(3q-1) = (3q)^2 - (1)^2
  4. Simplify expression: Simplify (3q)2−(1)2.(3q)^2 - (1)^2.(3q)2−(1)2=(3q×3q)−(1×1)(3q)^2 - (1)^2 = (3q \times 3q) - (1 \times 1)=9q2−1= 9q^2 - 1

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