Math: Advanced Math

SAT Question of the Day for November 3, 2026

Which of the following is equivalent to (4x+11)(4x−11)(4x + 11)(4x - 11)?
  1. A.8x2−1218x^2 - 121
  2. B.16x2+12116x^2 + 121
  3. C.16x2−12116x^2 - 121Correct answer
  4. D.4x2−1214x^2 - 121

Explanation

The correct answer is 16x2−12116x^2 - 121. This expression is a difference of squares: (a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2. Here a=4xa = 4x and b=11b = 11, so (4x)2−112=16x2−121(4x)^2 - 11^2 = 16x^2 - 121. The result 4x2−1214x^2 - 121 incorrectly computes (4x)2(4x)^2 as 4x24x^2, squaring only the variable and not the coefficient. The result 8x2−1218x^2 - 121 confuses squaring with doubling, computing 2⋅4x2=8x22 \cdot 4x^2 = 8x^2 instead of (4x)2=16x2(4x)^2 = 16x^2. The result 16x2+12116x^2 + 121 uses a sum of squares instead of a difference, ignoring the opposite signs in the factors.

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