Question

(2x² - 5)²
use the pattern for difference of two squares.
answer: 4x⁴ - 25
explain what is incorrect.

calculate the correct answer below.

Explanation:

The expression \((2x^2 - 5)^2\) is a perfect square trinomial, not a difference of two squares. The difference of two squares formula is \(a^2 - b^2=(a + b)(a - b)\), while squaring a binomial \((a - b)^2\) uses the formula \(a^2-2ab + b^2\). The incorrect answer used the difference of squares pattern instead of the square of a binomial pattern, missing the middle term \(-2\times(2x^2)\times5=-20x^2\).

To find the correct answer, we use the formula for squaring a binomial \((a - b)^2=a^2-2ab + b^2\), where \(a = 2x^2\) and \(b = 5\).

Step-by-Step Calculation:

Step 1: Identify \(a\) and \(b\)

Here, \(a = 2x^2\) and \(b = 5\).

Step 2: Apply the square of a binomial formula

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Answer:

The incorrect part is using the difference of two squares pattern for a square of a binomial. The correct answer is \(4x^4-20x^2 + 25\).