Final answer:
To find the second expression, we can use the formula for the LCM of two expressions: LCM(A, B) = (A * B) / HCF(A, B). Given that the HCF is x and the first expression is ⁴ˣ(ⁿ+ᵃ)², we can substitute these values into the formula. We also know that the LCM is ⁴ˣ^²(ⁿ+ᵃ)²(ˣ²-ᵃ²), so we can equate the two expressions and solve for B.
Step-by-step explanation:
To find the second expression, we need to use the relation between the HCF and LCM of two numbers. The HCF is x and the LCM is ⁴ˣ²(ⁿ+ᵃ)²(ˣ² - ᵃ²). If the first expression is ⁴ˣ(ⁿ+ᵃ)², then the second expression can be found by dividing the LCM by the first expression. So, the second expression is ⁴ˣ(ⁿ+ᵃ)²(ˣ² - ᵃ²) ÷ ⁴ˣ(ⁿ+ᵃ)², which simplifies to ˣ² - ᵃ².