(4x² - 9)(4x² + 9) = 0 equation is equivalent to f(x) = 16x⁴ – 81 = 0.
The quadratic expression is defined as an expression containing the highest power of a variable is two.
Given equation as :
f(x) = 16x⁴ – 81 = 0
Difference of squares would be used to solve this equation. There are three perfect squares: 16, x4, and 81. ( which means that it is a number multiplied by itself, 16 is 4 x4 for example). Therefore, the first step is to remember the formula, which is (a² - b²) = (a - b)(a + b)
⇒ 16x⁴ – 81 = 0
Determine the square root of 16 which is 4, and of x⁴ which is x², and 81 which is 9.
Now rewrite the equation in the (a - b)(a + b) format :
⇒ (4x² - 9)(4x² + 9) = 0
Hence, (4x² - 9)(4x² + 9) = 0 equation is equivalent to given equation.
Learn more about quadratic expression here:
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